chapter 1 - fundamentals 1.7 - inequalities. rules for inequalities 1.7 - inequalities

1.7 - Inequalities

Section 1.7 Inequalities

Chapter 1 - Fundamentals

1.7 - Inequalities

Rules for Inequalities

1.7 - Inequalities

Linear InequalitiesAn inequality is linear if each term is constant or a

multiple of the variable.

To solve a linear inequality we isolate the variable on one side of the inequality sign.

1.7 - Inequalities

Example 1 – pg 80 # 20

Solve the linear inequality. Express the solution using interval notation and graph the solution set.

6 2 9x x

1.7 - Inequalities

Example 2 – pg 80 # 30

Solve the linear inequality. Express the solution using interval notation and graph the solution set.

1 3 4 16x

1.7 - Inequalities

Nonlinear Inequalities

Nonlinear inequalities are inequalities that involve squares or other powers of the variable other than 1.

1.7 - Inequalities

Solving Nonlinear Inequalities

1.7 - Inequalities

Example 3Solve the nonlinear inequality. Express the solution using

interval notation and graph the solution set.

1.

2.

3. 4.

3 5 0x x

22 15x x

50

7

x

x

1

23

x

x

1.7 - Inequalities

Absolute Value Inequalities

We use the following properties to solve absolute value inequalities.

1.7 - Inequalities

Example 4 – pg. 80Solve the absolute value inequality. Express the

answer using interval notation and graph the solution set.

81.

83.

3 2 5x

22

3

x