Introduction to Solving Inequalities

Objective: Write, solve, and graph linear inequalities in one variable.

Example 1

Example 1

Example 2

Example 2

Example 2

Try This

• Solve 5 – 7t > 8 – 4t. Graph the solution on a number line.

Try This

• Solve 5 – 7t > 8 – 4t. Graph the solution on a number line.

• Add 4t to both sides.• Subt. 5 from both sides.• Divide by -3, change the inequality sign.

1

33

835

4875

t

t

t

tt

Try This

• Solve 5 – 7t > 8 – 4t. Graph the solution on a number line.

• Add 4t to both sides.• Subt. 5 from both sides.• Divide by -3, change the inequality sign.• Graph.

1

33

835

4875

t

t

t

tt

01

Example 3

Example 3

Example 3

Example 4

• When solving an inequality involving the word and, you need to find the values of the variable that satisfy both inequalities. Usually your answer will be in between two numbers. We will see this in example 4.

Example 4

Example 4

Example 4

Try This

• Solve the following inequality. Graph the solution.

1622 and 543 xx

Try This

• Solve the following inequality. Graph the solution.

1622 and 543 xx

3

93

543

x

x

x

7

142

1622

x

x

x

and

3 7

Example 5

• When solving an inequality involving the word or, you need to find those values of the variable that satisfy at least one of the inequalities. In other words, one or the other. Usually, the answer is the two extremes. This is shown in example 5.

Example 5

Example 5

Example 5

Try This

• Solve the following inequality. Graph the solution.

3617or 52 xx

Try This

• Solve the following inequality. Graph the solution.

3617or 52 xx

25

52

x

x

5

357

3617

x

x

x

or

25 5

Homework

• Pages 58-59• 11-55 odd