$n1
+ x =
$n2
$d
$d
−$n1
−$n1
$d
$d
x =
$n
$d
Solve the equation:
x + $a = $b
@ qu.1.1.answer.num=$ans@ qu.1.1.answer.units=@ qu.1.1.showUnits=false@ qu.1.1.grading=exact_value@ qu.1.1.negStyle=minus@ qu.1.1.numStyle=thousands scientific dollars arithmetic@ qu.1.1.mode=Numeric@ qu.1.1.name=x + a = b@ qu.1.1.comment=Solve the equation:
x + $a = $b
Subtract $a from both sides.
| x + $a | = | $b |
−$a |
−$a | |
x |
= | $ans |
Solve the equation:
x − $a = $b
@ qu.1.2.answer.num=$ans@ qu.1.2.answer.units=@ qu.1.2.showUnits=false@ qu.1.2.grading=exact_value@ qu.1.2.negStyle=minus@ qu.1.2.numStyle=thousands scientific dollars arithmetic@ qu.1.2.mode=Numeric@ qu.1.2.name=x - a = b@ qu.1.2.comment=Solve the equation:
x − $a = $b
Add $a to both sides.
| x − $a | = | $b |
+$a |
+$a | |
x |
= | $ans |
Solve the equation:
$b = y − $a
@ qu.1.3.answer.num=$ans@ qu.1.3.answer.units=@ qu.1.3.showUnits=false@ qu.1.3.grading=exact_value@ qu.1.3.negStyle=minus@ qu.1.3.numStyle=thousands scientific dollars arithmetic@ qu.1.3.mode=Numeric@ qu.1.3.name=b = y - a@ qu.1.3.comment=Solve the equation:
$b = y − $a
Add $a to both sides.
| $b | = | y − $a |
+$a |
+$a |
|
$ans |
= | y |
Solve the equation:
$b = y + $a
@ qu.1.4.answer.num=$ans@ qu.1.4.answer.units=@ qu.1.4.showUnits=false@ qu.1.4.grading=exact_value@ qu.1.4.negStyle=minus@ qu.1.4.numStyle=thousands scientific dollars arithmetic@ qu.1.4.mode=Numeric@ qu.1.4.name=b = y + a@ qu.1.4.comment=Solve the equation:
$b = y + $a
Subtract $a from both sides.
| $b | = | y + $a |
−$a |
−$a |
|
$ans |
= | y |
Solve the equation:
$b = $a + z
@ qu.1.5.answer.num=$ans@ qu.1.5.answer.units=@ qu.1.5.showUnits=false@ qu.1.5.grading=exact_value@ qu.1.5.negStyle=minus@ qu.1.5.numStyle=thousands scientific dollars arithmetic@ qu.1.5.mode=Numeric@ qu.1.5.name=b = a + z@ qu.1.5.comment=Solve the equation:
$b = $a + z
Subtract $a from both sides.
| $b | = | $a + z |
| −$a | −$a |
|
$ans |
= | z |
Solve the equation:
$a + z = $b
@ qu.1.6.answer.num=$ans@ qu.1.6.answer.units=@ qu.1.6.showUnits=false@ qu.1.6.grading=exact_value@ qu.1.6.negStyle=minus@ qu.1.6.numStyle=thousands scientific dollars arithmetic@ qu.1.6.mode=Numeric@ qu.1.6.name=a + z = b@ qu.1.6.comment=Solve the equation:
$a + z = $b
Subtract $a from both sides.
| $a + z | = | $b |
−$a |
−$a | |
z |
= | $ans |
Solve the equation:
x + $a = $b
@ qu.2.1.answer.num=$ans@ qu.2.1.answer.units=@ qu.2.1.showUnits=false@ qu.2.1.grading=exact_value@ qu.2.1.negStyle=minus@ qu.2.1.numStyle=thousands scientific dollars arithmetic@ qu.2.1.mode=Numeric@ qu.2.1.name=x + a = b@ qu.2.1.comment=Solve the equation:
x + $a = $b
Subtract $a from both sides.
| x + $a | = | $b |
−$a |
−$a | |
x |
= | $ans |
Solve the equation:
x − $a = $b
@ qu.2.2.answer.num=$ans@ qu.2.2.answer.units=@ qu.2.2.showUnits=false@ qu.2.2.grading=exact_value@ qu.2.2.negStyle=minus@ qu.2.2.numStyle=thousands scientific dollars arithmetic@ qu.2.2.mode=Numeric@ qu.2.2.name=x - a = b@ qu.2.2.comment=Solve the equation:
x − $a = $b
Add $a to both sides.
| x − $a | = | $b |
+$a |
+$a | |
x |
= | $ans |
Solve the equation:
$b = y − $a
@ qu.2.3.answer.num=$ans@ qu.2.3.answer.units=@ qu.2.3.showUnits=false@ qu.2.3.grading=exact_value@ qu.2.3.negStyle=minus@ qu.2.3.numStyle=thousands scientific dollars arithmetic@ qu.2.3.mode=Numeric@ qu.2.3.name=b = y - a@ qu.2.3.comment=Solve the equation:
$b = y − $a
Add $a to both sides.
| $b | = | y − $a |
+$a |
+$a |
|
$ans |
= | y |
Solve the equation:
$b = y + $a
@ qu.2.4.answer.num=$ans@ qu.2.4.answer.units=@ qu.2.4.showUnits=false@ qu.2.4.grading=exact_value@ qu.2.4.negStyle=minus@ qu.2.4.numStyle=thousands scientific dollars arithmetic@ qu.2.4.mode=Numeric@ qu.2.4.name=b = y + a@ qu.2.4.comment=Solve the equation:
$b = y + $a
Subtract $a from both sides.
| $b | = | y + $a |
−$a |
−$a |
|
$ans |
= | y |
Solve the equation:
$b = $a + z
@ qu.2.5.answer.num=$ans@ qu.2.5.answer.units=@ qu.2.5.showUnits=false@ qu.2.5.grading=exact_value@ qu.2.5.negStyle=minus@ qu.2.5.numStyle=thousands scientific dollars arithmetic@ qu.2.5.mode=Numeric@ qu.2.5.name=b = a + z@ qu.2.5.comment=Solve the equation:
$b = $a + z
Subtract $a from both sides.
| $b | = | $a + z |
| −$a | −$a |
|
$ans |
= | z |
Solve the equation:
$a + z = $b
@ qu.2.6.answer.num=$ans@ qu.2.6.answer.units=@ qu.2.6.showUnits=false@ qu.2.6.grading=exact_value@ qu.2.6.negStyle=minus@ qu.2.6.numStyle=thousands scientific dollars arithmetic@ qu.2.6.mode=Numeric@ qu.2.6.name=a + z = b@ qu.2.6.comment=Solve the equation:
$a + z = $b
Subtract $a from both sides.
| $a + z | = | $b |
−$a |
−$a | |
z |
= | $ans |
Solve:
${mathml("$n1/$d+x=$n2/$d")}
| Subtract $n1/$d from both sides. | |||
$n1 |
+ x = |
$n2
|
|
|
|
||
$d |
$d
|
||
−$n1 |
−$n1 |
||
|
|
||
$d |
$d |
||
x = |
$n |
||
|
|||
$d |
|||
${if(gt($g,1),"The fraction may be reduced by dividing numerator and denominator by ","")} ${if(gt($g,1), $g,"")}${if(gt($g,1),"","The fraction cannot be reduced")}.
x = $ans
@ qu.3.1.editing=useHTML@ qu.3.1.algorithm=$d=range(3,8,1); $n1=range(1,$d-1,1); $n22=range(1,$d-1,1); $n2=range(-1,1,2)*$n22; condition:eq(gcd($n1,$d),1); condition:eq(gcd($n2,$d),1); condition:ne($n1,$n2); $n=$n2-$n1; $g=gcd($n,$d); $ans=frac($n,$d); condition:ne($n,0);@ qu.3.1.question=Solve:
${mathml("$n1/$d+x=$n2/$d")}
x = <1>
Enter an integer or a reduced fraction as 3/11 or 7/4 with no spaces in the answer box.
@ qu.3.1.blank.1=%24ans@ qu.3.1.extra=@ qu.3.1.format.input=text@ qu.3.2.mode=Blanks@ qu.3.2.name=a + x = b (a neg)@ qu.3.2.comment=Solve:
${mathml("$n1/$d+x=$n2/$d")}
| Add $negn1/$d to both sides. | |||
$n1 |
+ x = |
$n2
|
|
|
|
||
$d |
$d
|
||
$negn1 |
$negn1 |
||
|
|
||
$d |
$d |
||
x = |
$n |
||
|
|||
$d |
|||
${if(gt($g,1),"The fraction may be reduced by dividing numerator and denominator by ","")} ${if(gt($g,1), $g,"")}${if(gt($g,1),"","The fraction cannot be reduced")}.
x = $ans
@ qu.3.2.editing=useHTML@ qu.3.2.algorithm=$d=range(3,8,1); $n1=range(-$d+1,-1,1); $n22=range(1,$d-1,1); $n2=range(-1,1,2)*$n22; condition:eq(gcd($n1,$d),1); condition:eq(gcd($n2,$d),1); condition:ne($n1,$n2); $n=$n2-$n1; $negn1=-1*$n1; $g=gcd($n,$d); $ans=frac($n,$d); condition:ne($n,0);@ qu.3.2.question=Solve:
${mathml("$n1/$d+x=$n2/$d")}
x = <1>
Enter an integer or a reduced fraction as 3/11 or 7/4 with no spaces in the answer box.
@ qu.3.2.blank.1=%24ans@ qu.3.2.extra=@ qu.3.2.format.input=text@ qu.3.3.mode=Blanks@ qu.3.3.name=x - a = b@ qu.3.3.comment=Solve:
${mathml("x-$n1/$d=$n2/$d")}
Add $n1/$d to both sides.
| x − |
|
= |
|
||||||
|
|
||||||||
x = |
|
${if(gt($g,1),"The fraction may be reduced by dividing numerator and denominator by ","")} ${if(gt($g,1), $g,"")}${if(gt($g,1),"","The fraction cannot be reduced")}.
x = $ans
@ qu.3.3.editing=useHTML@ qu.3.3.algorithm=$d=range(3,8,1); $n1=range(1,$d-1,1); $n22=range(1,$d-1,1); $n2=range(-1,1,2)*$n22; condition:eq(gcd($n1,$d),1); condition:eq(gcd($n2,$d),1); condition:ne($n1,$n2); $n=$n2+$n1; $negn1=-1*$n1; $g=gcd($n,$d); $ans=frac($n,$d); condition:ne($n,0);@ qu.3.3.question=Solve:
${mathml("x-$n1/$d=$n2/$d")}
x = <1>
Enter an integer or a reduced fraction as 3/11 or 7/4 with no spaces in the answer box.
@ qu.3.3.blank.1=%24ans@ qu.3.3.extra=@ qu.3.3.format.input=text@ qu.3.4.mode=Blanks@ qu.3.4.name=b = x - a@ qu.3.4.comment=Solve:
${mathml("$n2/$d=x-$n1/$d")}
Add $n1/$d to both sides.
|
= | x − |
|
||||||
|
|
||||||||
|
= x |
${if(gt($g,1),"The fraction may be reduced by dividing numerator and denominator by ","")} ${if(gt($g,1), $g,"")}${if(gt($g,1),"","The fraction cannot be reduced")}.
x = $ans
@ qu.3.4.editing=useHTML@ qu.3.4.algorithm=$d=range(3,8,1); $n1=range(1,$d-1,1); $n22=range(1,$d-1,1); $n2=range(-1,1,2)*$n22; condition:eq(gcd($n1,$d),1); condition:eq(gcd($n2,$d),1); condition:ne($n1,$n2); $n=$n2+$n1; $negn1=-1*$n1; $g=gcd($n,$d); $ans=frac($n,$d); condition:ne($n,0);@ qu.3.4.question=Solve:
${mathml("$n2/$d=x-$n1/$d")}
x = <1>
Enter an integer or a reduced fraction as 3/11 or 7/4 with no spaces in the answer box.
@ qu.3.4.blank.1=%24ans@ qu.3.4.extra=@ qu.3.4.format.input=text@ qu.3.5.mode=Blanks@ qu.3.5.name=b = x + a@ qu.3.5.comment=Solve:
${mathml("$n2/$d=x+$n1/$d")}
Subtract $n1/$d from both sides.
|
= | x + |
|
||||||
|
|
||||||||
|
= x |
${if(gt($g,1),"The fraction may be reduced by dividing numerator and denominator by ","")} ${if(gt($g,1), $g,"")}${if(gt($g,1),"","The fraction cannot be reduced")}.
x = $ans
@ qu.3.5.editing=useHTML@ qu.3.5.algorithm=$d=range(3,8,1); $n1=range(1,$d-1,1); $n22=range(1,$d-1,1); $n2=range(-1,1,2)*$n22; condition:eq(gcd($n1,$d),1); condition:eq(gcd($n2,$d),1); condition:ne($n1,$n2); $n=$n2-$n1; $negn1=-1*$n1; $g=gcd($n,$d); $ans=frac($n,$d); condition:ne($n,0);@ qu.3.5.question=Solve:
${mathml("$n2/$d=x+$n1/$d")}
x = <1>
Enter an integer or a reduced fraction as 3/11 or 7/4 with no spaces in the answer box.
@ qu.3.5.blank.1=%24ans@ qu.3.5.extra=@ qu.3.5.format.input=text@ qu.4.topic=3_2 Solve by Div - Int Sol@ qu.4.1.question=Solve:
${$a}x = $b
@ qu.4.1.answer.num=$ans@ qu.4.1.answer.units=@ qu.4.1.showUnits=false@ qu.4.1.grading=exact_value@ qu.4.1.negStyle=minus@ qu.4.1.numStyle=thousands scientific dollars arithmetic@ qu.4.1.mode=Numeric@ qu.4.1.name=ax = b + + = +@ qu.4.1.comment=Solve:
${$a}x = $b
Divide both sides by $a.
${$a}x |
= |
$b |
|
|
|
$a |
$a |
x = $ans
@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=$a=range(2,12,1); $ans=range(2,12,1); $b=$a*$ans;@ qu.4.2.question=Solve:
${$a}x = $b
@ qu.4.2.answer.num=$ans@ qu.4.2.answer.units=@ qu.4.2.showUnits=false@ qu.4.2.grading=exact_value@ qu.4.2.negStyle=minus@ qu.4.2.numStyle=thousands scientific dollars arithmetic@ qu.4.2.mode=Numeric@ qu.4.2.name=ax = b - + = -@ qu.4.2.comment=Solve:
${$a}x = $b
Divide both sides by $a.
${$a}x |
= |
$b |
|
|
|
$a |
$a |
x = $ans
@ qu.4.2.editing=useHTML@ qu.4.2.algorithm=$a=range(-12,-2,1); $ans=range(2,12,1); $b=$a*$ans;@ qu.4.3.question=Solve:
$b = ${$a}x
@ qu.4.3.answer.num=$ans@ qu.4.3.answer.units=@ qu.4.3.showUnits=false@ qu.4.3.grading=exact_value@ qu.4.3.negStyle=minus@ qu.4.3.numStyle=thousands scientific dollars arithmetic@ qu.4.3.mode=Numeric@ qu.4.3.name=b = ax + = - -@ qu.4.3.comment=Solve:
$b = ${$a}x
Divide both sides by $a.
$b |
= |
${$a}x |
|
|
|
$a |
$a |
$ans = x
@ qu.4.3.editing=useHTML@ qu.4.3.algorithm=$a=range(-12,-2,1); $ans=range(-12,-2,1); $b=$a*$ans;@ qu.4.4.question=Solve:
$b = ${$a}x
@ qu.4.4.answer.num=$ans@ qu.4.4.answer.units=@ qu.4.4.showUnits=false@ qu.4.4.grading=exact_value@ qu.4.4.negStyle=minus@ qu.4.4.numStyle=thousands scientific dollars arithmetic@ qu.4.4.mode=Numeric@ qu.4.4.name=b = ax - = + -@ qu.4.4.comment=Solve:
$b = ${$a}x
Divide both sides by $a.
$b |
= |
${$a}x |
|
|
|
$a |
$a |
$ans = x
@ qu.4.4.editing=useHTML@ qu.4.4.algorithm=$a=range(2,12,1); $ans=range(-12,-2,1); $b=$a*$ans;@ qu.5.topic=3_2 Solve by Div - Decimals@ qu.5.1.question=Solve:
${$a}x = $b
Round answers to the nearest 0.01.
@ qu.5.1.answer.num=$ans@ qu.5.1.answer.units=@ qu.5.1.showUnits=false@ qu.5.1.grading=exact_value@ qu.5.1.negStyle=minus@ qu.5.1.numStyle=thousands scientific dollars arithmetic@ qu.5.1.mode=Numeric@ qu.5.1.name=ax = b + + = +@ qu.5.1.comment=Solve:
${$a}x = $b
Divide both sides by $a.
${$a}x |
= |
$b |
|
|
|
$a |
$a |
x = $ans
@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=$a=range(2,12,.01); $an=range(2,12,.01); $b=decimal(2,$a*$an);$ans=decimal(2,$b/$a);@ qu.5.2.question=Solve:
${$a}x = $b
Round answers to the nearest 0.01.
@ qu.5.2.answer.num=$ans@ qu.5.2.answer.units=@ qu.5.2.showUnits=false@ qu.5.2.grading=exact_value@ qu.5.2.negStyle=minus@ qu.5.2.numStyle=thousands scientific dollars arithmetic@ qu.5.2.mode=Numeric@ qu.5.2.name=ax = b - + = -@ qu.5.2.comment=Solve:
${$a}x = $b
Divide both sides by $a.
${$a}x |
= |
$b |
|
|
|
$a |
$a |
x = $ans
@ qu.5.2.editing=useHTML@ qu.5.2.algorithm=$a=range(-12,-2,.01); $an=range(2,12,.01); $b=decimal(2,$a*$an);$ans=decimal(2,$b/$a);@ qu.5.3.question=Solve:
$b = ${$a}x
Round answers to the nearest 0.01.
@ qu.5.3.answer.num=$ans@ qu.5.3.answer.units=@ qu.5.3.showUnits=false@ qu.5.3.grading=exact_value@ qu.5.3.negStyle=minus@ qu.5.3.numStyle=thousands scientific dollars arithmetic@ qu.5.3.mode=Numeric@ qu.5.3.name=b = ax + = - -@ qu.5.3.comment=Solve:
$b = ${$a}x
Divide both sides by $a.
$b |
= |
${$a}x |
|
|
|
$a |
$a |
$ans = x
@ qu.5.3.editing=useHTML@ qu.5.3.algorithm=$a=range(-12,-2,.01); $an=range(-12,-2,.01); $b=decimal(2,$a*$an);$ans=decimal(2,$b/$a);@ qu.5.4.question=Solve:
$b = ${$a}x
Round answers to the nearest 0.01.
@ qu.5.4.answer.num=$ans@ qu.5.4.answer.units=@ qu.5.4.showUnits=false@ qu.5.4.grading=exact_value@ qu.5.4.negStyle=minus@ qu.5.4.numStyle=thousands scientific dollars arithmetic@ qu.5.4.mode=Numeric@ qu.5.4.name=b = ax - = + -@ qu.5.4.comment=Solve:
$b = ${$a}x
Divide both sides by $a.
$b |
= |
${$a}x |
|
|
|
$a |
$a |
$ans = x
@ qu.5.4.editing=useHTML@ qu.5.4.algorithm=$a=range(2,12,.01); $an=range(-12,-2,.01); $b=decimal(2,$a*$an);$ans=decimal(2,$b/$a);@ qu.6.topic=3_2 Solve by Mult - Integers@ qu.6.1.question=Solve:
$x |
= $b | ||
|
|||
$a |
Solve:
$x |
= $b | ||
|
|||
$a |
Multiply both sides by $a.
| $a • | $x |
= $b | • $a |
|
|||
$a |
x = $ans
@ qu.6.1.editing=useHTML@ qu.6.1.algorithm=$a=range(2,12,1); $b=range(2,12,1); $ans=$a*$b;@ qu.6.2.question=Solve:
$x |
= $b | ||
|
|||
$a |
Solve:
$x |
= $b | ||
|
|||
$a |
Multiply both sides by $a.
| $a • | $x |
= $b | • $a |
|
|||
$a |
x = $ans
@ qu.6.2.editing=useHTML@ qu.6.2.algorithm=$a=range(2,12,1); $b=range(-12,-1,1); $ans=$a*$b;@ qu.6.3.question=Solve:
| $b = | $x |
||
|
|||
$a |
Solve:
| $b = | $x |
||
|
|||
$a |
Multiply both sides by $a.
| $a • | $b = | $x |
• $a |
|
|||
$a |
$ans = x
@ qu.6.3.editing=useHTML@ qu.6.3.algorithm=$a=range(-12,-2,1); $b=range(-12,-2,1); $ans=$a*$b;@ qu.6.4.question=Solve:
| $b = | $x |
||
|
|||
$a |
Solve:
| $b = | $x |
||
|
|||
$a |
Multiply both sides by $a.
| $a • | $b = | $x |
• $a |
|
|||
$a |
$ans = x
@ qu.6.4.editing=useHTML@ qu.6.4.algorithm=$a=range(-12,-2,1); $b=range(2,12,1); $ans=$a*$b;@ qu.7.topic=3_2 Solve by Mult - Decimals@ qu.7.1.question=Solve:
$x |
= $b | ||
|
|||
$a |
Answers should be accurate to the nearest 0.01.
@ qu.7.1.answer.num=$ans@ qu.7.1.answer.units=@ qu.7.1.showUnits=false@ qu.7.1.grading=exact_value@ qu.7.1.negStyle=minus@ qu.7.1.numStyle=thousands scientific dollars arithmetic@ qu.7.1.mode=Numeric@ qu.7.1.name=x/a = b +/+ = +@ qu.7.1.comment=Solve:
$x |
= $b | ||
|
|||
$a |
Multiply both sides by $a.
| $a • | $x |
= $b | • $a |
|
|||
$a |
x = $ans
@ qu.7.1.editing=useHTML@ qu.7.1.algorithm=$a=range(2,12,0.1); $b=range(2,12,0.1); $ans=$a*$b;@ qu.7.2.question=Solve:
$x |
= $b | ||
|
|||
$a |
Answers should be accurate to the nearest 0.01.
@ qu.7.2.answer.num=$ans@ qu.7.2.answer.units=@ qu.7.2.showUnits=false@ qu.7.2.grading=exact_value@ qu.7.2.negStyle=minus@ qu.7.2.numStyle=thousands scientific dollars arithmetic@ qu.7.2.mode=Numeric@ qu.7.2.name=x/a = b -/+ = -@ qu.7.2.comment=Solve:
$x |
= $b | ||
|
|||
$a |
Multiply both sides by $a.
| $a • | $x |
= $b | • $a |
|
|||
$a |
x = $ans
@ qu.7.2.editing=useHTML@ qu.7.2.algorithm=$a=range(2,12,0.1); $b=range(-12,-2,.1); $ans=$a*$b;@ qu.7.3.question=Solve:
| $b = | $x |
||
|
|||
$a |
Answers should be accurate to the nearest 0.01.
@ qu.7.3.answer.num=$ans@ qu.7.3.answer.units=@ qu.7.3.showUnits=false@ qu.7.3.grading=exact_value@ qu.7.3.negStyle=minus@ qu.7.3.numStyle=thousands scientific dollars arithmetic@ qu.7.3.mode=Numeric@ qu.7.3.name=b = x/a - = +/-@ qu.7.3.comment=Solve:
| $b = | $x |
||
|
|||
$a |
Multiply both sides by $a.
| $a • | $b = | $x |
• $a |
|
|||
$a |
$ans = x
@ qu.7.3.editing=useHTML@ qu.7.3.algorithm=$a=range(-12,-2,.1); $b=range(-12,-2,.1); $ans=$a*$b;@ qu.7.4.question=Solve:
| $b = | $x |
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|
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$a |
Answers should be accurate to the nearest 0.01.
@ qu.7.4.answer.num=$ans@ qu.7.4.answer.units=@ qu.7.4.showUnits=false@ qu.7.4.grading=exact_value@ qu.7.4.negStyle=minus@ qu.7.4.numStyle=thousands scientific dollars arithmetic@ qu.7.4.mode=Numeric@ qu.7.4.name=b = x/a + = -/-@ qu.7.4.comment=Solve:
| $b = | $x |
||
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$a |
Multiply both sides by $a.
| $a • | $b = | $x |
• $a |
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$a |
$ans = x
@ qu.7.4.editing=useHTML@ qu.7.4.algorithm=$a=range(-12,-2,.1); $b=range(2,12,0.1); $ans=$a*$b;@ qu.8.topic=3_3 Solve Algebraically A@ qu.8.1.question=Solve algebraically.
${$a}x + $b = $c
Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x + $b = $c
Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x + $b = $c
Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x + $b = $c
Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a.
x = $x
Solve algebraically.
$b − ${-1*$a}x = $c
Solve algebraically.
$b − ${-1*$a}x = $c
Subtract $b from both sides.
$b − $b − ${-1*$a}x = $c − $b
${$a}x = ${$c - $b}
Divide by $a.
x = $x
Solve algebraically.
$b − ${-1*$a}x = $c
Solve algebraically.
$b − ${-1*$a}x = $c
Subtract $b from both sides.
$b − $b −
${-1*$a}x = $c − $b
${$a}x = ${$c - $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x − $b = $c
Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x − $b = $c
Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x − $b = $c
Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x − $b = $c
Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a.
x = $x
Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a.
Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x + $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.1.blank.1=%24an%2f%24ad@ qu.9.1.extra=@ qu.9.1.format.input=text@ qu.9.2.mode=Blanks@ qu.9.2.name=ax+b=c x-@ qu.9.2.comment=Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x + $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.2.blank.1=%24an%2f%24ad@ qu.9.2.extra=@ qu.9.2.format.input=text@ qu.9.3.mode=Blanks@ qu.9.3.name=-ax+b=c x+@ qu.9.3.comment=Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x + $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.3.blank.1=%24an%2f%24ad@ qu.9.3.extra=@ qu.9.3.format.input=text@ qu.9.4.mode=Blanks@ qu.9.4.name=-ax+b=c x-@ qu.9.4.comment= Solve algebraically.
${$a}x + $b = $c
Subtract $b from both sides.
${$a}x + $b − $b = $c − $b
${$a}x = ${$c - $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x + $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.4.blank.1=%24an%2f%24ad@ qu.9.4.extra=@ qu.9.4.format.input=text@ qu.9.5.mode=Blanks@ qu.9.5.name=b-ax=c x+@ qu.9.5.comment=Solve algebraically.
$b − ${-1*$a}x = $c
Subtract $b from both sides.
$b − $b − ${-1*$a}x = $c − $b
${$a}x = ${$c - $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
$b − ${-1*$a}x = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.5.blank.1=%24an%2f%24ad@ qu.9.5.extra=@ qu.9.5.format.input=text@ qu.9.6.mode=Blanks@ qu.9.6.name=b-ax=c x-@ qu.9.6.comment=Solve algebraically.
$b − ${-1*$a}x = $c
Subtract $b from both sides.
$b − $b − ${-1*$a}x = $c − $b
${$a}x = ${$c - $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
$b − ${-1*$a}x = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.6.blank.1=%24an%2f%24ad@ qu.9.6.extra=@ qu.9.6.format.input=text@ qu.9.7.mode=Blanks@ qu.9.7.name=-ax-b=c x+@ qu.9.7.comment=Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x − $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.7.blank.1=%24an%2f%24ad@ qu.9.7.extra=@ qu.9.7.format.input=text@ qu.9.8.mode=Blanks@ qu.9.8.name=-ax-b=c x-@ qu.9.8.comment=Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x − $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.8.blank.1=%24an%2f%24ad@ qu.9.8.extra=@ qu.9.8.format.input=text@ qu.9.9.mode=Blanks@ qu.9.9.name=ax-b=c x-@ qu.9.9.comment=Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x − $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.9.blank.1=%24an%2f%24ad@ qu.9.9.extra=@ qu.9.9.format.input=text@ qu.9.10.mode=Blanks@ qu.9.10.name=ax-b=c x+@ qu.9.10.comment=Solve algebraically.
${$a}x − $b = $c
Add $b to both sides.
${$a}x − $b + $b = $c + $b
${$a}x = ${$c + $b}
Divide by $a. Reduce the fraction if possible.
x = $an/$ad
Solve algebraically.
${$a}x − $b = $c
Write the answer as an integer or fraction in reduced form.
x = <1>
@ qu.9.10.blank.1=%24an%2f%24ad@ qu.9.10.extra=@ qu.9.10.format.input=text@ qu.10.topic=3_3 Solve Algebraically C@ qu.10.1.question=Solve:
| $b = | $x |
+ $c | |
|
|||
$a |
Solve:
| $b = | $x |
+ $c | |
|
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$a |
| $b − $c = | $x |
+ $c − $c | |
|
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$a |
| ${$b-$c} = | $x |
||
|
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$a |
| $a • | (${$b-$c}) = | $x |
• $a |
|
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$a |
Solve:
| $b = | $x |
+ $c | |
|
|||
$a |
Solve:
| $b = | $x |
+ $c | |
|
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$a |
| $b − $c = | $x |
+ $c − $c | |
|
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$a |
| ${$b-$c} = | $x |
||
|
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$a |
| ($a) • | (${$b-$c}) = | $x |
• ($a) |
|
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$a |
Solve:
| $b = | $x |
− $c | |
|
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$a |
| $b + $c = | $x |
− $c + $c | |
|
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$a |
| ${$b+$c} = | $x |
||
|
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$a |
| $a • | (${$b+$c}) = | $x |
• $a |
|
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$a |
Solve:
| $b = | $x |
− $c | |
|
|||
$a |
Solve:
| $b = | $x |
− $c | |
|
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$a |
| $b + $c = | $x |
− $c + $c | |
|
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$a |
| ${$b+$c} = | $x |
||
|
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$a |
| ($a) • | (${$b+$c}) = | $x |
• ($a) |
|
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$a |
Solve:
$x |
+ $c | = $b | |
|
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$a |
Solve:
$x |
+ $c | = $b | |
|
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$a |
$x |
+ $c − $c | = $b − $c | |
|
|||
$a |
$x |
= ${$b - $c} | ||
|
|||
$a |
| ($a) • | $x |
= ${$b - $c} • ($a) | |
|
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$a |
Solve:
$x |
− $c | = $b | |
|
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$a |
Solve:
$x |
− $c | = $b | |
|
|||
$a |
$x |
− $c + $c | = $b + $c | |
|
|||
$a |
$x |
= ${$b + $c} | ||
|
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$a |
| ($a) • | $x |
= ${$b + $c} • ($a) | |
|
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$a |
Write an equation and solve:
Student Council has a goal of collecting $c pounds of paper for a recycling project. They have already collected $b pounds of paper and have $m weeks left in the paper drive. How many pounds of paper must be collected per week?
@ qu.11.1.answer.num=$ans@ qu.11.1.answer.units=@ qu.11.1.showUnits=false@ qu.11.1.grading=exact_value@ qu.11.1.negStyle=minus@ qu.11.1.numStyle=thousands scientific dollars arithmetic@ qu.11.1.mode=Numeric@ qu.11.1.name=Paper@ qu.11.1.comment=Student Council has a goal of collecting $c pounds of paper for a recycling project. They have already collected $b pounds of paper and have $m weeks left in the paper drive. How many pounds of paper must be collected per week?
Let p = the pounds of paper needed per week.
Current paper + weeks • pounds per week = total paper
$b + ${$m}p = $c
Solve for p.
$b − $b + ${$m}p = $c − $b
${$m}p = ${$c-$b}
p = $ans
Write an equation and solve:
Gretchen pays 
$b for a cell phone. She pays $m for each minute of cell phone use. Her last bill was $c. How many minutes did she talk on the cell phone?
Write an equation and solve:
Gretchen pays $b for a cell phone. She pays $m for each minute of cell phone use. Her last bill was $c. How many minutes did she talk on the cell phone?
Let m = the minutes of cell phone use
monthly rate + minutes • cost per minute = total bill
$b + ${$m}m = $c
Solve for m.
$b − $b + ${$m}m = $c − $b
${$m}m = ${$c-$b}
m = $ans
Write an equation and solve:
Juan is planning to purchase a $c high-definition TV. He will make a down payment of $b and then make $m payments monthly. How many months will it take to pay off the TV?
Write an equation and solve:
Juan is planning to purchase a $c high-definition TV. He will make a down payment of $b and then make $m payments monthly. How many months will it take to pay off the TV?
Let m = the months of payments
down payment + payment per month • months of payments = cost of TV
$b + ${$m}m = $c
Solve for m.
$b − $b + ${$m}m = $c − $b
${$m}m = ${$c-$b}
m = $ans
Write an equation and solve:
Juan is planning to purchase a $c high-definition TV. He will make a down payment of $b and then make $m payments monthly. How many months will it take to pay off the TV?
Write an equation and solve:
Ms. Peters has$b in a savings account. She is planning to withdraw a certain amount each week over the next $m weeks. How much should be withdrawn weekly so that $c will remain after $m weeks?
Let w = withdrawal amount
starting amount − weeks • withdrawal = ending amount
$b − ${$m}w = $c
Solve for w.
$b − $b − ${$m}w = $c − $b
${-1*$m}w = ${$c-$b}
w = $ans
Write an equation and solve:
The population of Welkerville is currently $b. The population is decreasing at $m residents per year. How many years will it take for the population to reach $c.
@ qu.11.5.answer.num=$ans@ qu.11.5.answer.units=@ qu.11.5.showUnits=false@ qu.11.5.grading=exact_value@ qu.11.5.negStyle=minus@ qu.11.5.numStyle=thousands scientific dollars arithmetic@ qu.11.5.mode=Numeric@ qu.11.5.name=Population@ qu.11.5.comment=Write an equation and solve:
The population of Welkerville is currently $b. The population is decreasing at $m residents per year. How many years will it take for the population to reach $c.
Let y = the number of years
current population − decrease in population per year • number of years = ending population
$b − ${$m}y = $c
Solve for y.
$b − $b − ${$m}y = $c − $b
${-1*$m}y = ${$c-$b}
y = $ans
Find the area of the rectangle or square.
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$w in |
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$l in |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
@ qu.12.1.answer.num=$area@ qu.12.1.answer.units=in^2@ qu.12.1.showUnits=true@ qu.12.1.grading=exact_value@ qu.12.1.negStyle=minus@ qu.12.1.numStyle=thousands scientific dollars arithmetic@ qu.12.1.mode=Numeric@ qu.12.1.name=Rectangle@ qu.12.1.comment=Find the area of the rectangle or square.
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$w in |
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$l in |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
Area = Length 
Width
Area = $l in $w in.
Area = $area in2 entered as $area in^2
Find the area of the rectangle or square.
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$s cm |
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$s cm |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
@ qu.12.2.answer.num=$area@ qu.12.2.answer.units=cm^2@ qu.12.2.showUnits=true@ qu.12.2.grading=exact_value@ qu.12.2.negStyle=minus@ qu.12.2.numStyle=thousands scientific dollars arithmetic@ qu.12.2.mode=Numeric@ qu.12.2.name=Square@ qu.12.2.comment=Find the area of the rectangle or square.
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$s cm |
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$s cm |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
The area of a square is side side or s2.
Area = ($s cm)2
Area = $area cm2 entered as $area cm^2
Find the perimeter of the rectangle or square.
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$w in |
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$l in |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
@ qu.13.1.answer.num=$perimeter@ qu.13.1.answer.units=in@ qu.13.1.showUnits=true@ qu.13.1.grading=exact_value@ qu.13.1.negStyle=minus@ qu.13.1.numStyle=thousands scientific dollars arithmetic@ qu.13.1.mode=Numeric@ qu.13.1.name=Rectangle@ qu.13.1.comment=Find the perimeter of the rectangle or square.
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$w in |
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$l in |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
The perimeter of a rectangle is 2L + 2W.
P = 2$l in + 2$w in
P = ${2*$l} in + ${2*$w} in
P = $perimeter in
Find the perimeter of the rectangle or square.
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$s cm |
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$s cm |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
@ qu.13.2.answer.num=$perimeter@ qu.13.2.answer.units=cm@ qu.13.2.showUnits=true@ qu.13.2.grading=exact_value@ qu.13.2.negStyle=minus@ qu.13.2.numStyle=thousands scientific dollars arithmetic@ qu.13.2.mode=Numeric@ qu.13.2.name=Square@ qu.13.2.comment=Find the perimeter of the rectangle or square.
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$s cm |
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$s cm |
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Enter units. To enter a square such as m2, use the ^ key as m^2.
The perimeter of a square is 2L + 2W.
P = 2$s cm + 2$s cm
P = ${2*$s} cm + ${2*$s} cm
P = $perimeter cm
Find the area of the triangle. Answers should be accurate to the nearest 0.01.
Enter units for the area. ft2 should be entered with the ^ as ft^2
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$h cm |
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$s cm |
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$s cm |
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$b cm |
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Find the area of the triangle. Answers should be accurate to the nearest 0.01.
Enter units for the area. ft2 should be entered with the ^ as ft^2
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$h cm |
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$s cm |
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$s cm |
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$b cm |
|
Area = ½ • base • height
Area = ½ • $b cm • $h cm
Area = $ans cm2 entered as $ans cm^2
Find the area of the triangle. Answers should be accurate to the nearest 0.01.
Enter units for the area. For example, ft2 should be entered with the ^ as ft^2
 |
$s ft |
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$b ft |
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$h ft |
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Find the area of the triangle. Answers should be accurate to the nearest 0.01.
Enter units for the area. For example, ft2 should be entered with the ^ as ft^2
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$s ft |
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$b ft |
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$h ft |
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Area = ½ • base • height
Area = ½ • $b ft • $h ft
Area = $ans ft2 entered as $ans ft^2
Find the area of the triangle. Answers should be accurate to the nearest 0.01.
Enter units for the area. For example, ft2 should be entered with the ^ as ft^2
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$s2 in |
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$s1 in |
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$h in |
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