1. Section 2.7 – Linear Inequalities and Absolute Value Inequalities

2. Inequalities and Intervals
Inequality
Graph
Interval 4. 5.

3. Linear Inequalities
Linear inequalities are solved exactly as a linear equation EXCEPT
If you multiply or divide by a negative, you must change the sense of the inequality!

4. Linear Inequality

5. Linear Inequality

6. Linear Inequality

7. Compound Inequalities
Compound Inequalities represent two inequalities in one statement.
Solve the conjunction by isolating the variable in the middle.
If you solve the inequalities separately, the solution will be the intersection of the two intervals.
Solve each inequality. The solution is the union of the two intervals.

8. Compound Inequalities – “or”

9. Compound Inequalities – “and”
Solve.
Isolate variable term in the center. You should perform the operations on ALL THREE PARTS of the inequality!

10. Absolute Value Inequalities
For a > 0 and an algebraic expression X:
|X| < a is equivalent to –a < X < a.
|X| > a is equivalent to X > a or X < -a
Solve and write interval notation for the solution set.

11. Absolute Value Inequalities