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GED Math : Solving for the Variable

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Example Questions

Example Question #31 : Solving For The Variable

Solve for :

$\frac{2}{7}y - \frac{3}{7} = \frac{1}{5}$

Possible Answers:

$y = \frac{5}{11}$

$y = \frac{44}{245}$

$y = 2 \frac{1}{5}$

$y = 5\frac{25 }{44}$

Correct answer:

$y = 2 \frac{1}{5}$

Explanation:

One way to solve a linear equation with fractional coefficients is to first multiply both sides by their least common denominator; this is the least common multiple of 5 and 7, which is 35, so multiply by this:

$\frac{2}{7}y - \frac{3}{7} = \frac{1}{5}$

$35 \cdot \left (\frac{2}{7}y - \frac{3}{7} \right ) = 35 \cdot \frac{1}{5}$

Since fractions are involved, change 35 to $\frac{35}{1}$ , and distribute on the left side:

$\frac{35}{1} \cdot \left (\frac{2}{7}y - \frac{3}{7} \right ) =\frac{35}{1} \cdot \frac{1}{5}$

$\frac{35}{1} \cdot \frac{2}{7}y - \frac{35}{1} \cdot \frac{3}{7} =\frac{35}{1} \cdot \frac{1}{5}$

Cross-cancel and multiply fractions across:

$\frac{5}{1} \cdot \frac{2}{1}y - \frac{5}{1} \cdot \frac{3}{1} =\frac{7}{1} \cdot \frac{1}{1}$

$\frac{10}{1}y - \frac{15}{1} =\frac{7}{1}$

10y -15 =7

Isolate on the left side by first adding 15 to both sides:

10y -15 + 15 =7 + 15

10y = 22

Divide both sides by 10:

$\frac{10y}{10} = \frac{22}{10}$

$y = 2\frac{2}{10} = 2 \frac{1}{5}$

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Example Question #31 : Solving For The Variable

Which of the following makes this equation true:

$\frac{y}{9} = 13$

Possible Answers:

y=4

y=6

y=117

y=99

y=118

Correct answer:

y=117

Explanation:

To answer the question, we will solve for y. We get

$\frac{y}{9} = 13$

$\frac{y}{9} \cdot 9 = 13 \cdot 9$

y = 117

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Example Question #32 : Solving For The Variable

Solve the equation: x+4 = 8-x

Possible Answers:

$\textup{No solution.}$

Correct answer:

Explanation:

Add on both sides.

x+4+x = 8-x+x

2x+4=8

Subtract 4 on both sides.

2x+4-4=8-4

2x=4

Divide by 2 on both sides.

$\frac{2x}{2}=\frac{4}{2}$

The answer is:

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Example Question #33 : Solving For The Variable

Solve for : y-3 = 2(y-2)

Possible Answers:

Correct answer:

Explanation:

Distribute the right side.

y-3 = 2y-4

Subtract on both sides.

y-3 -y= 2y-4-y

-3 = y-4

Add 4 on both sides.

-3 +4= y-4+4

The answer is: y=1

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Example Question #34 : Solving For The Variable

Solve for the variable: 9x-4 = 17

Possible Answers:

$\frac{7}{3}$

$\frac{7}{2}$

$\frac{13}{9}$

$\frac{9}{7}$

Correct answer:

$\frac{7}{3}$

Explanation:

Add 4 on both sides.

9x-4 +4= 17+4

9x=21

Divide by 9 on both sides.

$\frac{9x}{9}=\frac{21}{9}$

Reduce both sides.

The answer is: $\frac{7}{3}$

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Example Question #81 : Single Variable Algebra

Solve for the variable: x-7 = 2x-3

Possible Answers:

$-\frac{10}{3}$

$-\frac{4}{3}$

Correct answer:

Explanation:

Subtract from both sides.

x-7 -x= 2x-3-x

-7 = x-3

Add 3 on both sides.

-7 +3= x-3+3

x=-4

The answer is:

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Example Question #31 : Solving For The Variable

Give the solution set:

9 (x + 18) < 261

Possible Answers:

$\left \{ x| x< 27\right \}$

$\left \{ x| x< 11 \right \}$

$\left \{ x| x< 31\right \}$

$\left \{ x| x< 47\right \}$

Correct answer:

$\left \{ x| x< 11 \right \}$

Explanation:

First, distribute the 9 on the left by multiplying it by each expression in the parentheses:

9 (x + 18) < 261

$9 \cdot x + 9 \cdot 18 < 261$

9 x +162 < 261

Isolate on the right by first, subtracting 162 from both sides:

9 x +162 - 162 < 261 - 162

9 x < 99

Divide both sides by 9:

$\frac{9x }{9}< \frac{99}{9}$

x< 11

The correct solution set is $\left \{ x| x< 11 \right \}$ .

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Example Question #37 : Solving For The Variable

Which of the following makes this equation true:

12x+4=112

Possible Answers:

x=9

x=4

x=12

x=8

x=7

Correct answer:

x=9

Explanation:

To answer the question, we will solve for x. So, we get

12x+4=112

12x+4-4=112-4

12x=108

$\frac{12x}{12} = \frac{108}{12}$

x=9

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Example Question #82 : Single Variable Algebra

Solve for : 3x+5 = -19

Possible Answers:

$-\frac{14}{3}$

Correct answer:

Explanation:

Subtract five from both sides.

3x+5 -5= -19-5

3x=-24

Divide by three on both sides.

$\frac{3x}{3}=\frac{-24}{3}$

The answer is:

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Example Question #39 : Solving For The Variable

Solve the equation: -2x-3 = 4x-7

Possible Answers:

$\frac{2}{3}$

$-\frac{5}{3}$

$\frac{3}{2}$

$\frac{5}{4}$

$\frac{5}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

Add on both sides.

-2x-3 +2x= 4x-7+2x

-3 = 6x-7

Add 7 on both sides.

-3 +7= 6x-7+7

4= 6x

Divide by 6 on both sides.

$\frac{4}{6}= \frac{6x}{6}$

Reduce both fractions.

The answer is: $\frac{2}{3}$

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GED Math : Solving for the Variable

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #31 : Solving For The Variable

Example Question #31 : Solving For The Variable

Example Question #32 : Solving For The Variable

Example Question #33 : Solving For The Variable

Example Question #34 : Solving For The Variable

Example Question #81 : Single Variable Algebra

Example Question #31 : Solving For The Variable

Example Question #37 : Solving For The Variable

Example Question #82 : Single Variable Algebra

Example Question #39 : Solving For The Variable

All GED Math Resources

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