2.6 Absolute Value

Goals

SWBAT solve inequalities involving absolute value.

Definitions The of a,

denoted , is the distance that a is from zero on a number line.

The absolute value of a number is always.

  So, in other words, and . That

said, we must consider both the negative and positive versions of a when solving absolute value equations and inequalities.

absolute value

a

positive

a a a a

Solve.

1. x 4 7

Solve

2. 12 3n 27

Solving Absolute Value Inequalities 1. Get the absolute value by itself, making

sure to remember that if you or by a negative

you flip the sign! 2. Set up two equality problems, one for the

positive, one for the negative, and solve. 3. Plot your solution(s) on a number line. Use

an dot for < or >, and a

dot for or 4. Test the intervals on your number line to

determine where to shade. (shade where it makes the statement true)

5. Write a compound inequality for your solution. (an and or an or) 

multiplydivide

open closed

Solve the open set and graph its solution set.

3. v 5

2

Solve the open set and graph its solution set.

4. c 6 2

Solve the open set and graph its solution set.

5. 2n 9 7

Solve the open set and graph its solution set.

6. 1

3q 4 2

Solve the open set and graph its solution set.

7. 2 x 1

2 6

Solve the open set and graph its solution set.

8. 7 3c2

4