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Name_____________________ #5 - Absolute Value Equations and Inequalities Equations Goal: Solve for “x”. How To Do: 1. Isolate the absolute value expression. 2. Remove the absolute value symbols. 3. Rewrite as 2 equations. (one equals positive number & one equals negative number) 4. Solve each equation for “x”. 1. 3n 5 7 5. 5 2 x 4 10 2. 4 2 x 10 6. 3x 6 18 3. 11 5 3x 7 7. 2 x 7 9 21 4. 2 x 5 6 Inequalities Steps: To solve | ax+b |<c, solve the compound inequality –c<ax+b<c (think of this as a sANDwich inequality & that the solution set will be the intersection of the solution sets of ax+b>-c AND ax+b<c) -c 0 c To solve | ax+b |>c, solve the compound inequalities: ax+b<-c OR ax+b>c. (think of this – greater than means mORe than & the solution set will be the union of the solution sets of ax+b<-c & ax+b>c) -c 0 c Solve each absolute value inequality and graph on a number line. 1. |4x – 3| < 5 3. -3 2 x 6 1 8 2. 4 + |2x + 6| < 15 4. 2 3 2 x 1 20 2 3