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GED Math : Solving for the Variable

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Example Questions

Example Question #1 : Solving For The Variable

Solve for :

$\small \frac{n}{2}+4=10$

Possible Answers:

$\small n=3$

$\small n=28$

$\small n=12$

$\small n=7$

Correct answer:

$\small n=12$

Explanation:

$\small \frac{n}{2}+4=10$

$\small 2(\frac{n}{2}+4)=2(10)$

$\small n+8=20$

$\small n+8-8=20-8$

$\small n=12$

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Example Question #2 : Solving For The Variable

Solve for :

$\small \frac{n}{2}+4=3$

Possible Answers:

$\small n=-1$

$\small n=3$

$\small n=1$

$\small n=-2$

Correct answer:

$\small n=-2$

Explanation:

$\small \frac{n}{2}+4=3$

$\small 2(\frac{n}{2}+4)=2(3)$

$\small n+8=6$

$\small n+8-8=6-8$

$\small n=-2$

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Example Question #3 : Solving For The Variable

Two more than twice a number equals 9. What's the square of that number?

Possible Answers:

$\frac{49}{2}$

$\frac{49}{4}$

$\sqrt{\frac{7}{2}}$

$\frac{7}{2}$

Correct answer:

$\frac{49}{4}$

Explanation:

Rewrite the algebraic expression in a mathematical formula.

2x+2=9

Solve for x.

2x =7

$x= \frac{7}{2}$

The square of this number is:

$x^2 = \frac{49}{4}$

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Example Question #3 : Solving For The Variable

5(y + 4) +2 (y + 2) = 7y

Solve for .

Possible Answers:

y = 1

No solution

y = 24

y = 0

Correct answer:

No solution

Explanation:

5(y + 4) +2 (y + 2) = 7y

$5 \cdot y + 5 \cdot 4 +2 \cdot y +2 \cdot 2 = 7y$

5 y +20+2 y +4 = 7y

5 y +2 y +20+4 = 7y

7y +24 = 7y

7y - 7y+24 = 7y - 7y

24 = 0

Since the original statement forces this false statement to be true, the original statement is false regardless of the value of . There is no solution.

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Example Question #3 : Solving For The Variable

Solve the inequality for :

$6-\frac{x}{3} > 8$

Possible Answers:

$\left (6, \infty \right )$

$\left (42, \infty \right )$

$\left ( -\infty ,-6 \right )$

$\left ( -\infty ,-42 \right )$

Correct answer:

$\left ( -\infty ,-6 \right )$

Explanation:

$6-\frac{x}{3} > 8$

$6-\frac{x}{3}- 6 > 8 - 6$

$-\frac{x}{3} > 2$

$-\frac{x}{3} \cdot (-3) < 2 \cdot (-3)$ - note the switch in the inequality symbol

x < -6

That is, $\left ( -\infty ,-6 \right )$ .

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Example Question #4 : Solving For The Variable

Give the solution set of the inequality:

7y + 10 > 3y + 12

Possible Answers:

$\left (2, \infty \right )$

$\left ( 5 \frac{1}{2}, \infty \right )$

$\left ( \frac{1}{2}, \infty \right )$

$\left ( \frac{1}{5}, \infty \right )$

Correct answer:

$\left ( \frac{1}{2}, \infty \right )$

Explanation:

7y + 10 > 3y + 12

7y + 10 - 3y > 3y + 12 - 3y

4y + 10 > 12

4y + 10 - 10> 12 - 10

4y > 2

$4y\div 4 > 2\div 4$

$y > \frac{1}{2}$

In interval form, this is $\left ( \frac{1}{2}, \infty \right )$ .

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Example Question #54 : Single Variable Algebra

Solve for :

$t + \frac{1}{6} = \frac{4}{3}$

Possible Answers:

$t = \frac{7}{6}$

$t = \frac{2}{9}$

$t = \frac{3}{2}$

t = 1

Correct answer:

$t = \frac{7}{6}$

Explanation:

$t + \frac{1}{6} = \frac{4}{3}$

$t + \frac{1}{6} - \frac{1}{6} = \frac{4}{3} - \frac{1}{6}$

$t = \frac{4}{3} - \frac{1}{6} = \frac{4 \cdot 2 }{3 \cdot 2 } - \frac{1}{6} = \frac{8}{6} - \frac{1}{6} = \frac{7}{6}$

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Example Question #4 : Solving For The Variable

Give the solution set of the inequality:

$7y + 10 \leq -3y + 24$

Possible Answers:

$\left ( -\infty, 1.4 \right ]$

$\left ( -\infty, -1.4 \right ]$

$\left ( -\infty, 3.5 \right ]$

$\left ( -\infty, - 3.5 \right ]$

Correct answer:

$\left ( -\infty, 1.4 \right ]$

Explanation:

$7y + 10 \leq -3y + 24$

$7y + 10 + 3y \leq -3y + 24 + 3y$

$10y + 10 \leq 24$

$10y + 10- 10 \leq 24 - 10$

$10y \leq 14$

$10y \div 10 \leq 14 \div 10$

$y \leq 1.4$

or, in interval form, $\left ( -\infty, 1.4 \right ]$

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Example Question #4 : Solving For The Variable

Consider the expression $\frac{7-3N}{17 - 2N}$ .

What value, if substituted in for , makes this expression undefined?

Possible Answers:

$N = \frac{3}{7}$

$N = \frac{2}{17}$

$N = 8 \frac{1}{2}$

$N = 2\frac{1}{3}$

Correct answer:

$N = 8 \frac{1}{2}$

Explanation:

$\frac{7-3N}{17 - 2N}$ is undefined if and only if its denominator is equal to 0.

17 - 2N = 0

2N = 17

$\frac{2N }{2}= \frac{17}{2}$

$N = 8 \frac{1}{2}$

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Example Question #5 : Solving For The Variable

Solve for :

$\frac{1}{4} t = \frac{5}{8}$

Possible Answers:

$t = \frac{2}{5}$

$t = \frac{5}{32}$

$t = \frac{5}{2}$

$t = \frac{32}{5}$

Correct answer:

$t = \frac{5}{2}$

Explanation:

$\frac{1}{4} t = \frac{5}{8}$

Multiply both sides by 4 to isolate :

$\frac{4}{1}\cdot \frac{1}{4} t =\frac{4}{1}\cdot \frac{5}{8}$

$t =\frac{4\cdot 5}{1 \cdot 8} = \frac{20}{8} = \frac{20 \div 4}{8 \div 4} = \frac{5}{2}$

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All GED Math Resources

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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 #1 : Solving For The Variable

Example Question #2 : Solving For The Variable

Example Question #3 : Solving For The Variable

Example Question #3 : Solving For The Variable

Example Question #3 : Solving For The Variable

Example Question #4 : Solving For The Variable

Example Question #54 : Single Variable Algebra

Example Question #4 : Solving For The Variable

Example Question #4 : Solving For The Variable

Example Question #5 : Solving For The Variable

All GED Math Resources

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