3-6 Absolute Value Equations and Inequalities Hubarth Algebra

Solving Absolute Value Equations *Note* an absolute value can never equal 0

Ex 1 Solving Absolute Value Equations Solve and check |a| – 3 = 5. First, get the absolute value by itself |a| – 3 + 3 = 5 + 3 Add 3 to each side. |a| = 8 Simplify. Second set the absolute value equal to itself and its opposite a = 8 or a = –8 Definition of absolute value.

Ex 2 Solving an Absolute Value Equation Solve |3c – 6| = 9. The absolute value is by itself, set equal to itself and its opposite 3c – 6 = 9 3c – 6 = –9 3c – 6 + 6 = 9 + 6 3c – 6 + 6 = –9 + 6 3c = 15 3c = –3 3c 3 = 15 –3 c = 5 c = –1 The value of c is 5 or –1.

Solving Absolute Value Inequalities You solve absolute value inequalities the same as equations. The only difference is you must also flip the inequality when solving.

Ex 3 Solving an Absolute Value Inequality Solve |y – 5| 2. Graph the solutions. <

Practice -1, 1 -5, 5 6, -6 -4, 8 -2, 2 no solution w<-7 or w>3 -7 3