Which of the following values of x satisfy the inequality |6 - 3x| > 9? Select all that ap… — GRE General Test

Which of the following values of $x$ satisfy the inequality $|6 - 3x| > 9$ ? Select all that apply.

The values

-4

-2

, and

6

satisfy the inequality

|6 - 3x| > 9

The absolute value inequality

|6 - 3x| > 9

is equivalent to

6 - 3x > 9

6 - 3x < -9

. Solving these yields

x < -1

x > 5

. Among the given choices,

-4

-2

, and

6

fall within these solution ranges.

Set up the compound linear inequalities from the absolute value inequality

|6 - 3x| > 9

6 - 3x > 9

6 - 3x < -9

An absolute value inequality of the form

|u| > c

(where

c > 0

) splits into

u > c

u < -c

Solve the first inequality

6 - 3x > 9

-3x > 3 \implies x < -1

Subtracting

6

gives

-3x > 3

. Dividing both sides by

-3

reverses the inequality sign to yield

x < -1

Solve the second inequality

6 - 3x < -9

-3x < -15 \implies x > 5

Subtracting

6

gives

-3x < -15

. Dividing both sides by

-3

reverses the inequality sign to yield

x > 5

Combine the solution sets and evaluate the given options.

The solution set consists of all real numbers where

x < -1

x > 5

. Therefore,

-4

-2

, and

6

are valid solutions.

Values

-4

and

-2

are strictly less than

-1

, while

6

is strictly greater than

5

Solving absolute value inequalities and reversing inequality signs when multiplying or dividing by negative numbers.

Question