Chapter 1: Equations and Inequalities

Lesson 4: Solving Absolute Value Equations

Absolute Value

Absolute Value: of a number is its distance from 0 on the number line.

The distance is always nonnegativeHow far is -5 from 0?

Absolute Value

The symbol lxI represents the absolute value of a number

For any real number a, if a is positive or 0 the abs value of a is a. If a is negative, the abs value of a is the opposite of a.

IaI = a, if a ≥ 0, and IaI = -a if a < 0.

Example 1:

Evaluate: 1.4 + I5y - 7I if y = -31.4 + I5y-7I = 1.4 + I5 (-3) -7I replace y w/ -3

= 1.4 + I-15 - 7I simplify 5 (-3) first = 1.4 + I-22I Subtract 7 from -15

= 1.4 + 22 I-22I = 22

= 23.4 add

See example #2

Note:

The absolute value is always positive.So the solution for the equation IxI = -5 is

an empty set or ø See examples

Homework: Pg. 30, #15-47 odd

Classwork: Pg. 29, #1-14