### Solving Inequalities

Inequalities – Inequality problems will have a less than or greater than sign.

There may often be more than one inequality or equation in a single problem on the math part of the test.

The second equation may have the equal sign rather than an inequality sign, as in the examples in the next section.

### Solving Inequalities – Practice Exercises

Have a look at the inequality problems below.

**Exercise 1:**

In the equations below, *x* represents the cost of one online game and *y* represents the cost of one discounted movie ticket.

If *x* − 2 > 5

and *y* = *x* − 2

Then the cost of 2 discounted movie tickets is greater than which one of the following?

A. *x* − 2

B. *x* − 5

C. *y* + 5

D. 5

E. 10

**The correct answer is E.**

For problems like this, look to see if both of the equations have any variables or terms in common.

In this problem, both equations contain *x* − 2.

The cost of one movie ticket is represented by *y* and *y* is equal to *x* − 2.

Therefore, we can substitute values from one equation to another.

*x* − 2 > 5

*y* > 5

If two tickets are being purchased, we need to solve for 2*y.*

*y* × 2 > 5 × 2

2*y* > 10

**Exercise 2:**

If *x* – 1 > 0 and *y* = *x* – 1, then *y* > ?

A. *x*

B. *x* + 1

C. *x* – 1

D. 1

E. 0

**The correct answer is E .**

Notice that both equations contain *x* – 1.

Therefore, we can substitute y for *x* – 1 in the first equation.

x – 1 > 0

*x* – 1 = *y*

*y* > 0