Notes 3.7B – ABSOLUTE VALUE INEQUALITIES

Absolute ValueIf ABSOLUTE VALUE represents the distance a number is from zero, means all x values that are 3 units from zero.  If given , what are some values that make this true?

What does mean?

1, 2,0, 2.5,

ALL x VALUES LESS THAN 3 UNITS FROM 0.

3x

3x

3x

1, 2, 2.9999

 If given , what are some values that make this true?

What does mean?

5, 6,4,

ALL x VALUES GREATER THAN 3 UNITS FROM 0.

3x

3x

4, 5, 6

Solving and Absolute Value Inequalities:

To solve and inequality in the form | A | < b where A is a variable expression and b > 0, solve the compound inequality:Graph:

For

Graph:

.b A b

b b

,A b .b A b

b b

Solving and Absolute Value Inequalities:

To solve and inequality in the form | A | > b where A is a variable expression and b > 0, solve the compound inequality:

Graph:

For

Graph:

b b

OR .A b A b

,A b OR .A b A b

b b

 In General with Absolute Value Inequalities:

LESS THAN means “WITHIN”

GREATER(GREAT “OR”) THAN means EITHER/OR

Examples: Solve and Graph the following inequalities:

1) 3 5x+ <

5 3 5x 3 3 3

8 2x

LESS THAN

MEANS "WITHIN"

8 2

2) 4 12y+ >

4 12 OR 4 12y y 4 4

8y OR 16y

GREAT"OR" THAN

MEANS "EITHER/OR"

4 4

16 8

3) 3

4

y

12 12y

LESS THAN

MEANS "WITHIN"

12 12

4 34

y

12y

4) 3 2 1 5x- + £ -

1 4 OR 1 4x x 3 3

3x OR 5x

GREAT"OR" THAN

MEANS "EITHER/OR"

2 2

5 3

2 1 8x- + £ -

1 4x+ ³

1 1 1 1

Homework :

Section 3.7B pages 228-229 #’s 6-24 EVEN, 25-28 ALL