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GED Math : Solving for the Variable

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Example Questions

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Example Question #61 : Single Variable Algebra

Give the solution set of the inequality:

-7y + 10 > 3y + 12

Possible Answers:

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

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

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

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

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 : Single Variable Algebra

Solve for :

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

Possible Answers:

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

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

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

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

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 #13 : Solving For The Variable

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

Possible Answers:

(-12, 8)

(-8, 12)

(-33, 13)

(-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 #14 : Solving For The Variable

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 #61 : 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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Example Question #61 : Algebra

If 5(x-5) = 50 , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

The first step in the process of solving for in this problem is to use the distributive property to distribute the to what is inside the parentheses.

5x - 25

The next step is to isolate the variable by using inverse operations. In this example, in order to get rid of the , you would add to both sides of the equation.

5x - 25 + 25 = 50 + 25

5x = 75

The next step is to divide both sides by the coefficient, (the number next to the variable), which in this case is .

$\frac{5x}{5} = x$

$\frac{75}{5} = 15$

x = 15

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Example Question #61 : Algebra

If x + 12 = 30 , then what is the value of ?

Possible Answers:

Correct answer:

Explanation:

In order to solve for the value of you must isolate the variable. This is done by subtracting the constant in this equation, which is 12, from both sides of the equation.

x + 12 - 12 = 30 - 12

x = 18

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Example Question #12 : Solving For The Variable

Solve for : 2x =-2y+7x

Possible Answers:

$x=-\frac{2}{5}y$

$x=-\frac{2}{9y}$

$x=-\frac{2}{9}y$

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

$x=-\frac{2}{5y}$

Correct answer:

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

Explanation:

In order to solve for , we will need the equation to be in terms of , and isolate the variable .

Solve by grouping the terms together. Subtract on both sides.

2x-(7x) =-2y+7x-(7x)

-5x = -2y

Divide by negative five on both sides.

$\frac{-5x }{-5}= \frac{-2y}{-5}$

The answer is: $x=\frac{2}{5}y$

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Example Question #19 : Solving For The Variable

Solve for : 2x+18 = -9(2x)+2x

Possible Answers:

$\frac{11}{18}$

$\textup{No solution.}$

Correct answer:

Explanation:

Distribute the term on the right side of the equation.

2x+18 = -18x+2x

Combine like terms.

2x+18 = -16x

Subtract on both sides.

2x+18 -2x= -16x-2x

18 = -18x

Divide by negative on both sides.

$\frac{18}{-18} = \frac{-18x}{-18}$

The answer is: x=-1

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Example Question #62 : Algebra

Which of the following makes this equation true:

12y-3=33

Possible Answers:

y=7

y=3

y=6

y=4

y=2

Correct answer:

y=3

Explanation:

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

12y-3=33

12-3+3=33+3

12y-0=36

12y=36

$\frac{12y}{12} = \frac{36}{12}$

y = 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 #61 : Single Variable Algebra

Example Question #62 : Single Variable Algebra

Example Question #13 : Solving For The Variable

Example Question #14 : Solving For The Variable

Example Question #61 : Algebra

Example Question #61 : Algebra

Example Question #61 : Algebra

Example Question #12 : Solving For The Variable

Example Question #19 : Solving For The Variable

Example Question #62 : Algebra

All GED Math Resources

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