Lesson 1-7 Solving Absolute-Value Equations Obj: The student will be able to solve equations in one variable that contain absolute-value expressions HWK: p even, even, all

Absolute-value – the distance a number is from zero | - 5 | = 5 | 5 | = 5 | - 7 | = | 7 | = How many solutions are there for any absolute value? So, | x | = a, then x = or x = ( a ≥ 0)

Steps 1)Isolate the absolute-value expression 2)Rewrite equation as two cases not involving absolute-value 3)Solve both cases

Solve each equation Ex 1) | x | = 4 Ex 2) | x | - 3 = 4 Ex 3) 4| x + 2 | = 24

Special Cases of Absolute-Value Equations If expression = 0, then one solution If expression = a negative number, then no solution

Solve each equation Ex 4) | x + 3 | + 4 = 4 Ex 5) 2 - | 2x – 5 | = 7 Ex 6) – 6 + | x – 4 | = -6

Ex 7) Sydney Harbour Bridge in Australia is 1149 meters long. Because of changes in temperatures, the bridge can expand or contract by as much as 420 millimeters. Write and solve an absolute-value equation to find the minimum and maximum lengths of the bridge.