Warm Up  Solve the equation or inequality.  1.) 3x + 15 = -42  2.) 5x – 8 ≤ 7  3.) 2x + 1 5

1.7 SOLVE ABSOLUTE VALUE EQUATIONS AND INEQUALITIES Algebra II

Objective  Solve absolute value equations.

Vocabulary  Absolute value – distance the number is from 0 on a number line. Absolute values are always positive.  Extraneous solutions – an apparent solution that must be rejected because it does not satisfy the original equation.

Steps to solve  Use these steps to solve an absolute value equation |ax + b| = c where c > 0.  Step 1) Write two equations: ax + b = c or ax + b = -c.  Step 2) Solve each equation.  Step 3) Check each solution in the original absolute value eqation.

Example 1 – Solve a simple absolute value equation  Solve |2x – 9| = 15. Graph the solutions.

Example 2 – Solve an absolute value equation  Solve |4x + 12| = 28.

Example 3 – Check for extraneous solutions.  Solve |4x + 10| = 6x. Check for extraneous solutions.

Assignment  Pg. 55 (4 – 38 even)