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GED Math : GED Math

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All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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:

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

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

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

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

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 #52 : Single Variable Algebra

Solve for :

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

Possible Answers:

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

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

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

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

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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Example Question #61 : Algebra

Give the solution set of the inequality:

-7y + 10 > 3y + 12

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

-7y + 10 > 3y + 12

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

-10y + 10 > 12

-10y + 10 - 10 > 12 - 10

-10y > 2

$-10y \div (-10) < 2 \div (-10)$

Note that the inequality symbol changes.

$y < -\frac{2}{10}$

$y < -\frac{1}{5}$

or, in interval notation, $\left ( -\infty, -\frac{1}{5} \right )$ .

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Example Question #62 : Algebra

Solve for :

$-\frac{2}{7} y \geq -4$

Possible Answers:

$\left [ -14, \infty \right)$

$\left [ - \frac{8}{7}, \infty \right)$

$\left ( -\infty , \frac{8}{7}\right ]$

$\left ( -\infty , 14\right ]$

Correct answer:

$\left ( -\infty , 14\right ]$

Explanation:

$-\frac{2}{7} y \geq -4$

$-\frac{2}{7} y \cdot\left ( -\frac{7} {2} \right ) \leq -4 \cdot\left ( -\frac{7} {2} \right )$

Note that the inequality symbol changes.

$y\leq \frac{28} {2}$

$y\leq 14$

or, in interval notation, $\left ( -\infty , 14\right ]$ .

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Example Question #63 : Algebra

$10 > 7-\frac{x}{4} > 5$

Possible Answers:

(-8, 12)

(-33, 13)

(-12, 8)

(-13, 33)

Correct answer:

(-12, 8)

Explanation:

$10 > 7-\frac{x}{4} > 5$

$10 - 7 > 7-\frac{x}{4} - 7 > 5 - 7$

$3 > -\frac{x}{4} > -2$

$3 \cdot (-4) < -\frac{x}{4} \cdot (-4) < -2 \cdot (-4)$

Note the switch in the inequality symbol.

-12< x< 8 .

This can also be written as (-12, 8) .

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Example Question #63 : Algebra

Which of the following is the solution set of the inequality $-13 \leq 8-3x \leq 20$ ?

Possible Answers:

$\left [ -4, 7\right ]$

$\left [ 4, 7\right ]$

$\left [ -7, 4 \right ]$

$\left [ -7, - 4 \right ]$

Correct answer:

$\left [ -4, 7\right ]$

Explanation:

Solve using the properties of inequality, as follows:

$-13 \leq 8-3x \leq 20$

$-13- 8 \leq 8-3x - 8 \leq 20 - 8$

$-21 \leq -3x \leq 12$

$-21 \div (-3) \geq -3x \div (-3) \geq 12 \div (-3)$

Note that division by a negative number reverses the symbols.

$7 \geq x\geq -4$

In interval form, this is $\left [ -4, 7\right ]$ .

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Example Question #65 : Algebra

If 7x + 6 = 27 , then 4x + 12 =

Possible Answers:

Correct answer:

Explanation:

To solve this you must find the value of .

The first equation states that 7x + 6 = 27 . This is a mult-step equation. The first step is to remove the constant, 6, from the equation; this is done by using the inverse operation, which means you would subtract the 6 from both sides of the equation.

7x + 6 - 6 = 27 -6

7x = 21

Then divide both sides by the 7 in order to isolate the variable.

$\frac{7x}{7}$ $=\frac{21}{7}$

x = 3

Then plug the 3 into the second equation for the value of x.

(4 x 3) + 12 = 24

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All GED Math Resources

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

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 #52 : Single Variable Algebra

Example Question #61 : Algebra

Example Question #62 : Algebra

Example Question #63 : Algebra

Example Question #63 : Algebra

Example Question #65 : Algebra

All GED Math Resources

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