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2.6 Absolute Value

2.6 Absolute Value. Goals SWBAT solve inequalities involving absolute value

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Page 1: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

2.6 Absolute Value

Page 2: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Goals

SWBAT solve inequalities involving absolute value.

Page 3: 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

Page 4: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve.

1. x 4 7

Page 5: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve

2. 12 3n 27

Page 6: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

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

Page 7: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve the open set and graph its solution set.

3. v 5

2

Page 8: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve the open set and graph its solution set.

4. c 6 2

Page 9: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve the open set and graph its solution set.

5. 2n 9 7

Page 10: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve the open set and graph its solution set.

6. 1

3q 4 2

Page 11: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve the open set and graph its solution set.

7. 2 x 1

2 6

Page 12: 2.6 Absolute Value. Goals  SWBAT solve inequalities involving absolute value

Solve the open set and graph its solution set.

8. 7 3c2

4