McGraw-Hill Education GRE 2019

Inequalities Versus Equations

The fundamental difference between equations and inequalities is the following:

Whereas an equation will give you a concrete value for a variable, an inequality

will only give you a range.

Compare:

x = 7 and x > 7

0

x = 7

7 0

x > 7

7

If you plot these on the number line, you will see that the equation x = 7 provides

one and only one value for x. On the other hand, the inequality x > 7 does not

provide a specific value; instead, it restricts the possible values that x can be.

Since x > 7, it can only be any number to the right of 7 on the number line.

Manipulating Inequalities

As is the case with equations, your initial goal with inequalities will usually be to

simplify what’s given to you. Fortunately, most of the rules you have learned for

manipulating equations will also apply to inequalities.

Addition and Subtraction with Inequalities

x + 3 > 12. Solve for x.

SOLUTION:

x + 3 > 12

− 3 − 3

x > 9

Here is another example:

If −x + 2y > y − 2x, then which of the following must be true? (Indicate all

that apply.)

A x > 0

B y > 0

C x + y > 0

CHAPTER 11 ■ ALGEBRA 301

03-GRE-Test-2018_173-312.indd 301 12/05/17 11:56 am