On the real number line, x is a real number such that |x + 2| \le 5. Which of the followin… — GRE General Test

On the real number line, $x$ is a real number such that $|x + 2| \le 5$ . Which of the following could be the value of $x$ ? Select all such values.

The values that satisfy the inequality are

-7

0

, and

3

The inequality

|x + 2| \le 5

represents all real numbers

x

whose distance from

-2

on the number line is at most

5

. This gives the closed interval

[-7, 3]

. The values

-7

0

, and

3

all fall within this range.

Set up the compound inequality for the absolute value expression.

-5 \le x + 2 \le 5

For any real number expression

A

and non-negative constant

k

|A| \le k

is equivalent to

-k \le A \le k

Isolate

x

by subtracting

2

from all parts of the inequality.

-5 - 2 \le x \le 5 - 2 \implies -7 \le x \le 3

Subtracting a constant from all parts preserves the inequality signs.

Evaluate which given choices lie within the interval

[-7, 3]

-7

0

, and

3

lie within

[-7, 3]

, while

-8

and

4

lie outside.

Only values inside or on the boundaries of

[-7, 3]

satisfy the inequality.

Absolute Value Inequalities and Real Number Line Distance

Question