If |x - 3| < 5, which of the following values could be the value of x? Select all such val… — GRE General Test

If $|x - 3| < 5$ , which of the following values could be the value of $x$ ? Select all such values.

The possible values of

x

are

-1

0

, and

4

The absolute value inequality

|x - 3| < 5

represents all real numbers

x

whose distance from

3

on the number line is strictly less than

5

. Expressed as a compound inequality, this means

-5 < x - 3 < 5

. Adding

3

across the entire inequality yields

-2 < x < 8

. The values

-1

0

, and

4

are the only options that fall strictly within the interval

(-2, 8)

Rewrite the absolute value inequality as a compound inequality.

-5 < x - 3 < 5

An absolute value inequality of the form

|u| < k

(where

k > 0

) is equivalent to

-k < u < k

Solve for

x

by adding

3

to all parts of the inequality.

-5 + 3 < x < 5 + 3 \implies -2 < x < 8

Adding a positive constant to all parts of an inequality isolates

x

while preserving inequality directions.

Test each given option against the range

-2 < x < 8

The values

-1

0

, and

4

lie within

(-2, 8)

, whereas

-3

and

8

lie outside.

-3

is less than or equal to

-2

, and

8

is not strictly less than

8

Solving linear absolute value inequalities

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