If |2x - 4| \le 6, which of the following values could be a solution for x? Select all tha… — GRE General Test

If $|2x - 4| \le 6$ , which of the following values could be a solution for $x$ ? Select all that apply.

The values

-1

2

, and

5

are solutions to the inequality.

Solving

|2x - 4| \le 6

yields

-6 \le 2x - 4 \le 6

. Adding

4

gives

-2 \le 2x \le 10

, and dividing by

2

gives

-1 \le x \le 5

. The options stating

-1

2

, and

5

are all within this interval

[-1, 5]

Rewrite the absolute value inequality as a compound inequality.

-6 \le 2x - 4 \le 6

An inequality of the form

|u| \le c

(where

c \ge 0

) is equivalent to

-c \le u \le c

Add

4

to all three parts of the compound inequality.

-2 \le 2x \le 10

Isolate the variable term

2x

in the middle.

Divide all three parts by

2

-1 \le x \le 5

Isolate

x

. Since

2

is positive, the inequality signs remain unchanged.

Test which of the given choices fall within the interval

[-1, 5]

-1

2

, and

5

lie within the range

[-1, 5]

, while

-3

and

6

lie outside.

Values equal to or between

-1

and

5

inclusive are valid solutions.

Linear Inequalities and Absolute Value

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