If |x - 4| = 9 and x < 0, what is the value of x? — GRE General Test

If $|x - 4| = 9$ and $x < 0$ , what is the value of $x$ ?

Answer: -5

The value of

x

-5

The absolute value equation

|x - 4| = 9

specifies that the distance between

x

and

4

on the real number line is equal to

9

. Moving

9

units to the left of

4

gives

4 - 9 = -5

, and moving

9

units to the right gives

4 + 9 = 13

. Because

x

is specified to be negative (

x < 0

), the correct value of

x

-5

Set up the two linear equations representing the absolute value equation

|x - 4| = 9

x - 4 = 9

x - 4 = -9

By definition,

|A| = B

(where

B \ge 0

) implies

A = B

A = -B

Solve for

x

in both equations.

x = 13

x = -5

Adding

4

to both sides of

x - 4 = 9

gives

x = 13

, and adding

4

to both sides of

x - 4 = -9

gives

x = -5

Select the value of

x

that satisfies the given condition

x < 0

x = -5

The value

13

is positive, while

-5

is negative and fulfills

x < 0

Absolute Value as Distance and Solving Absolute Value Equations

Estimated Time:45s

Question