1.6 Absolute-Value Equations & Inequalities

Absolute value of a number is its distance from zero on the number line. Absolute value of a number is never negative. If x ≥ 0, then |x| = x If x < 0, then |x| = -x

Properties of Absolute Value For any real number a and b |ab| = |a| |b| a |a| b |b| b ≠ 0 |-a| = |a| =

Simplify 1) |4x|= 2) |-4x 2 |= 3) |x 10 |= 4) |x 9 |= 5) 6x 3 = -3x 2

The distance between 2 numbers a and b is |a-b| or |b-a| 1) Find the distance between -8 and 1 Answer: 9 2) Find the distance between -6 and -35 Answer: 29

Solving equations with Absolute Value If |x| = p (p is positive) then x = -p or x = p If |x| = 0 then x = 0 If |x| = -p then there is no solution If |x| = |p| then x = -p or x = p

Examples On the black board

Solving inequalties with Absolute Value If |x| < p (p is positive) then -p < x < p If |x| > p then x p If |x| < -p then there is no solution

Examples On the black board