Algebra 1     27 17 105 Define the absolute value equation however you would like with your class. Copyright © 2011 Pearson Education, Inc.

Defining the Absolute-Value Function The absolute value of a number is its size, or magnitude, regardless of whether the number is positive or negative. A way to visualize the absolute value is the distance a number is from zero on the number line. Define the absolute value equation however you would like with your class. Copyright © 2011 Pearson Education, Inc.

The notation |x| is used to write absolute –value expressions The notation |x| is used to write absolute –value expressions. So you would write |3.2| = 3.2 and |-3.2| = 3.2

The absolute value of a number is always positive. | 3 | = 3 Absolute Value | 2.5 | = 2.5 | 0 | = | – 7 | = 7 | – 4.8 | = 4.8 True or False? The absolute value of a number is always positive. > 0 False Non-negative ≥ 0 The absolute value of a number is non-negative. The absolute value of a number is either positive or 0.

Absolute Value Equations | x | = 5 | x | = –2 Same Opposite No Solution x = 5 x = – 5 Two Solutions Absolute Value Equation If |x| = a, where x is a variable or an expression and a  0, then x = a or x = a.

Solving Absolute Value Equations 1. Isolate the absolute value so that the equation is in the form |ax + b| = c. If c < 0, the equation has no solution. 2. Separate the absolute value into two equations, ax + b = c and ax + b =  c. 3. Solve both equations.

Absolute Value Equations 1. Isolate 2. Two Cases 3. Solve Keep the absolute value bars! Same Opposite Drop the absolute value bars!

Absolute Value Equations 1. Isolate 2. Two Cases 3. Solve Keep the absolute value bars! Same Opposite Drop the absolute value bars!

Absolute Value Equations 1. Isolate 2. Two Cases 3. Solve No Solution

Absolute Value Equations 1. Isolate 2. Two Cases 3. Solve Same Opposite

Absolute Value Equations 1. Isolate 2. Two Cases 3. Solve Same Opposite Make sure students know they cannot distribute into a abs function

Solve these two problems correctly to receive your homework. 5, -13/2 & 20/7, -4 Copyright © 2011 Pearson Education, Inc.

HW: Absolute Value WS Copyright © 2011 Pearson Education, Inc.