Vocabularyinequalityalgebraic inequalitysolution set

1-9 Introduction to Inequalities

Course 3

An inequality compares two quantities and typically uses one of these symbols:

<is less than

is greater than

is less than or equal to

is greater than or equal to

1-9 Introduction to Inequalities

Course 3

An inequality that contains a variable is an algebraic inequality.

A number that makes an inequality true is a solution of the inequality.

The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line.

1-9 Introduction to Inequalities

Course 3

An open circle means that the corresponding value is not a solution. A solid circle means that the value is part of the solution set.

Helpful Hint!

1-9 Introduction to Inequalities

Course 3

x < 5

4 < 5x = 2.1 2.1 < 5

x is less than 5Word

Phrase

Inequality

Sample Solutions

Solution Set 1 2 3 4 5 6 7

x = 4

1-9 Introduction to Inequalities

Course 3

a > 0

7 > 0a = 25 25 > 0

a is greater than 0a is more than 0

Word Phrase

Inequality

Sample Solutions

Solution Set–3 –2 –1 0 1 2 3

a = 7

1-9 Introduction to Inequalities

Course 3

y 2

0 2y = 1.5 1.5 2

y is less than or equal to 2y is at most 2

Word Phrase

Inequality

Sample Solutions

Solution Set–3 –2 –1 0 1 2 3

y = 0

1-9 Introduction to Inequalities

Course 3

m 3

17 3m = 3 3 3

m is greater than or equal to 3m is at least 3

Word Phrase

Inequality

Sample Solutions

Solution Set–1 0 1 2 3 4 5

m = 17

1-9 Introduction to Inequalities

Course 3

Most inequalities can be solved the same way equations are solved.

Use inverse operations on both sides of the inequality to isolate the variable.

There are special rules when multiplying or dividing by a negative number but we will cover those in the next section.

1-9 Introduction to Inequalities

Course 3

The inequality symbol opens to the side with the greater number.

2 < 10

Remember!

1-9 Introduction to Inequalities

Course 3

Additional Example 2A: Solving and Graphing Inequalities

Solve and graph the inequality.

x + 2.5 8 –2.5 –2.5

x 5.5

1 2 3 4 5 6 7

Subtract 2.5 from both sides.

According to the graph, 5.4 is a solution, since 5.4 < 5.5, and 6 should not be solution because 6 > 5.5.

1-9 Introduction to Inequalities

Course 3

Additional Example 2B: Solving and Graphing Inequalities

Solve and graph the inequality.

w – 1 < 8

w < 9

–3 0 3 6 9 12 15

+ 1 + 1 Add 1 to both sides.

1-9 Introduction to Inequalities

Course 3

Check It Out: Example 2

Solve and graph each inequality.

7. x + 2 3.5 –2 –2x 1.5

1 2 3 4 5 6 7

Subtract 2 from both sides.

8. 6u > 72

6 6

u > 12 3 6 9 12 15 18 21

6u > 72 Divide both sides by 6.

1-9 Introduction to Inequalities

Course 3