#43

Solving One and Two-Step Inequalities

An inequality is a statement that two quantities are not equal. The quantitiesare compared by using one of the followingsymbols:

< > ≤ ≥ ≠An inequality may contain a variable, as in x > 3. A solution of an equality is any value of the variable that makes the statement true.

VOCABULARY

Graph the solutions of each inequality on a number line.

Example 1: Graphing Inequalities

2 3 4 5 6 7 8

A. t > 1

B. y 11

9 10 11 12 13 14 15

Solve and graph each inequality.

Example 2: Solving Inequalities with Addition or Subtraction

5 6 7 8 9 10 11432101–

x – 3 ≥ 5

Solve and graph each inequality.

Example 3

7654321

5 < x + 3

Solve and graph each inequality.

Example 4: Solving Inequalities with Multiplication or Division

5 6 7 8 9 10 11432101–

The empty circle at 4 shows that 4 is not a solution.

8z < 32

Graph the solution of the inequality on a number line.

Example 5

13 14 15 16 17 18 19

a 4 > 4

Example 6: Write an Inequality to Represent the SituationSix friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Example 7Derek must log at least 20 hours of flight time for a sport pilot certificate. So far, he has logged 7 hours. Write and solve an inequality to describe how much more flight time Derek needs to log.

Solve and graph each inequality.

Example 8: Solving Two-Step Inequalities

3y + 6 > 12

5 6 7 8 9 10 11432101–

Solve and graph each inequality.

Example 9: Solving Two-Step Inequalities

30 31 32 33 34 35 36292827262524

t 3 + 3 12

Solve and graph each inequality.

Example 10

2 m - 3 < 7

4 5 6 7 8 9 103210

The cost to rent a party room is $70. There is an additional fee of $8 per guest. How many guests can Jesse invite if he can spend no more than $150?

Example 11: Problem Solving Application

Hanley Ramirez plays baseball for the Florida Marlins. His batting average is his total hits divided by total at-bats, to the nearest thousandth. With two games remaining in the 2008 season, he had 173 hits and 581 at-bats. If he gets 8 more at-bats, how many more hits must he get to have an average of at least .300?

Example 12