6.4 Solving Absolute Value Equations and Inequalities Algebra 6.4 Solving Absolute Value Equations and Inequalities

Steps to Solve an Absolute Value Equation Isolate the absolute value expression Drop the absolute value and create a positive and a negative equation Solve each

Solving an Absolute Value Equation Solve lx – 4l = 8 x – 4 = 8 or x – 4 = -8 +4 +4 +4 +4 x = 12 or x = -4 Mentally check your answers.

Solving an Absolute Value Equation Solve l5x + 1l + 3 = 14 Isolate the absolute value expression. l5x + 1l = 11 5x + 1 = 11 or 5x + 1 = -11 -1 -1 -1 -1 5x = 10 or 5x = -12 x = 2 or x = - 2 and 2/5 Mentally check your answers. -3 -3 5 5

Investigating Absolute-Value Inequalities See if each number is a solution as it appears. If it is, fill it in. 1) lxl ≤ 2 (The distance from 0 is less than or equal to 2) 2) lxl > 3 (The distance from 0 is greater than 3) 3) lx + 2l ≥ 1 4) lx – 3l ≤ 2 . . . . . . . . . . . . . . . -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 x ≤ 2 and x ≥ -2 or . . . . . . . . . . . . . -5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 6 x > 3 or x < -3 WHY? and Absolute Value < or ≤ is an and inequality Absolute Value > or ≥ is an or inequality

Steps to Solve an Absolute Value Inequality Isolate the Absolute Value Expression Drop the absolute value and create a positive inequality and a negative inequality (flip the sign) Solve each inequality separately <, ≤ is an and inequality >, ≥ is an or inequality 5) Graph

Let’s Try! Solve lx + 6l < 8 x + 6 < 8 and x + 6 > -8 -6 -6 -6 -6 x < 2 and x > -14 -14 2

You Try! Solve l2x - 4l ≥ 2 2x - 4 ≥ 2 or 2x - 4 ≤ -2 +4 +4 +4 +4 +4 +4 +4 +4 2x ≥ 6 or 2x ≤ 2 x ≥ 3 or x ≤ 1 1 2 3

Let’s Try! Solve l2x + 1l - 3 ≥ 6 l2x + 1l – 3 ≥ 6 +3 +3 l2x + 1l ≥ 9 +3 +3 l2x + 1l ≥ 9 2x + 1 ≥ 9 or 2x + 1 ≤ -9 -1 -1 -1 -1 2x ≥ 8 or 2x ≤ -10 x ≥ 4 or x ≤ -5 -5 4

You Try! Solve l3x - 3l + 4 < 10 -4 -4 l3x - 3l < 6 3x - 3 < 6 and 3x - 3 > -6 +3 +3 +3 +3 3x < 9 and 3x > -3 x < 3 and x > -1 -1 3

HW P. 356-358 (19-59 Odd, 77-83 Odd)