Section 2.7 Absolute Value Equations and Inequalities

About Absolute Value The absolute value of a number is its distance from 0 on the number line. We use two vertical lines || to represent absolute value. Absolute value is always non-negative.

Absolute Value Equations Three cases: 1.k > 0. Then ax +b = k or ax + b = -k. Two solutions 2.k = 0. Then ax + b = 0. One solution. 3.k < 0. No Solution. You must isolate your absolute value expression first.

Absolute Value Inequalities ax + b > k or ax + b < -k ax + b -k You must isolate your absolute value expression first.

Examples

More Examples

Absolute Value on Both Sides |ax + b| = |cx + d| Write two equations: ax + b = cx + d ax + b = -(cx + d)