If x is an integer that satisfies the inequality |6 - 3x| - 4 \le 5, which of the followin… — GRE General Test

If $x$ is an integer that satisfies the inequality $|6 - 3x| - 4 \le 5$ , which of the following could be the value of $x$ ? Select all such values.

The correct values of

x

are

-1

2

, and

4

Isolating the absolute value yields

|6 - 3x| \le 9

, which expands to

-9 \le 6 - 3x \le 9

. Subtracting

6

gives

-15 \le -3x \le 3

. Dividing by

-3

and reversing the inequality signs results in

-1 \le x \le 5

. Among the given choices,

-1

2

, and

4

lie within this solution interval

[-1, 5]

Isolate the absolute value expression

|6 - 3x| \le 9

Add

4

to both sides of the inequality to isolate the absolute value term.

Rewrite as a compound inequality

-9 \le 6 - 3x \le 9

The property

|u| \le a

(where

a \ge 0

) expands to

-a \le u \le a

Subtract 6 from all parts

-15 \le -3x \le 3

Isolate the variable term

-3x

by subtracting

6

across the compound inequality.

Divide by -3 and reverse inequality signs

5 \ge x \ge -1

, which is equivalent to

-1 \le x \le 5

Dividing an inequality by a negative quantity requires flipping the inequality direction.

Solving absolute value inequalities of the form

|ax + b| \le c

by expanding into a compound inequality

-c \le ax + b \le c

and correctly reversing inequality signs when multiplying or dividing by negative numbers.

Question