McGraw-Hill Education GRE 2019

Step 1: Isolate the absolute value:

9 + |x + 4| = 28

−9 −9

|x + 4| = 19

Step 2: Create two equations. In one equation, the expression inside the

absolute value will equal the positive value on the right. In the other

equation, the expression inside the absolute value will equal the negative

version of the value on the right:

Equation 1 Equation 2

x + 4 = +(19) or x + 4 = −(19)

Step 3: Solve for the unknown in both equations:

Equation 1 Equation 2

x = 15 x = −23

Absolute Values and Inequalities

In tougher absolute value questions, you will be given a range for the absolute value

instead of a concrete value. For example:

|x| < 3 |x − 3| ≥ 6 |z + y| < 2

To solve these questions, take the following approach:

If |x + 3| < 7, what of the following describes the range for x?

Step 1: Set up two solutions:

(x + 3) < 7 and –(x + 3) < 7

− 3

x < 4

Step 2: Multiply by −1 (flip the sign!):

–(x + 3) < 7

↓

(x + 3) > −7

− 3 − 3

x > −10

CHAPTER 11 ■ ALGEBRA 305

03-GRE-Test-2018_173-312.indd 305 12/05/17 11:56 am