# Inequalities

### Solving Inequalities – ACT Math

Inequalities – Inequality problems on the ACT Math Exam 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

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 2y.

y × 2 > 5 × 2

2y   > 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

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