Section 2.7 – Linear Inequalities and Absolute Value Inequalities

Inequalities and Intervals Inequality Graph Interval 4. 5.

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!

Linear Inequality

Linear Inequality

Linear Inequality

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.

Compound Inequalities – “or”

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

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.

Absolute Value Inequalities