Absolute-Value Equations and Inequalities

Mental Math Solving

–Think What values could x be that would make the equation true? HINT: There are two!

–ANSWER: 5 or -5

Mental Math Solving (More Example)

• x = 7 or -7• x = 9 or -9• x = 18 or -18

Solving an Absolute-Value Equation

– This means that can equal 5 or -5.

x – 2 IS POSITIVE x – 2 IS NEGATIVE

SOLUTION: x = 7 or x = -3

Solving an Absolute-Value Equation

2x – 7 IS POSITIVE 2x – 7 IS NEGATIVE

POSITIVE NEGATIVE

IMPORTANT CHEAT SHEET

Solving Absolute-Value Equations and Inequalitiesax+b<c means ax+b<c AND ax+b>-cax+b≤c means ax+b≤c AND ax+b≥-cax+b=c means ax+b=c OR ax+b=-cax+b>c means ax+b>c OR ax+b<-cax+b≥c means ax+b≥c OR ax+b≤-c

Solving Absolute-Value Inequalities

• Remember that is the distance between and 0.• If , then any number between -8 and

8 is solution to the inequality.

x – 4 IS POSITIVE x – 4 IS NEGATIVE

Solution :1<x<7

2x + 1 IS POSITIVE 2x + 1 IS NEGATIVE

POSITIVE NEGATIVE

Notecard Check

Homework Assignment

• Pg. 356 – 357–Numbers: 24 – 36 and 46 – 46

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