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