Ch. 1-5 Absolute Value Equations and Inequalities

Ex. 1: Solve | 15 – 3x | = 6

| 15 – 3x | = 6

15 – 3x = 6 15 – 3x = -6-15 -15 -15 -15

-3x = -9 -3x = -21

x = 3 x = 7

Solve Check understanding 1 p. 33

Ex. 2: 4 – 2|x + 9| = -5

4 – 2|x + 9| = -5

-4 -4

-2|x + 9| = -9

99

2x

Ex. 3 cont.

99

2x

99

2x

-9 -9 -9 -9

x = -4.5 x = -13.5

Solve check understanding 2 p. 34

Ex. 3: Solve |3x – 4| = -4x - 1

3x – 4 = -4x – 1 3x – 4 = 4x + 1

+4x +4x

7x – 4 = -1

+4 +4

7x = 3

-3x -3x

-4 = x + 1-1 -1

x = -5

3

7x

When there is a variable outside of the absolute value, you must check your answers.

| 3(-5) – 4 | = -4(-5) -1

3

7x

| -15 – 4 | = 20 - 1

| -19 | = 19

19 = 19

x = -5

3 33 4 4 17 7

9 124 1

7 7

19 19

7 7

Solution Not a solution

Solve check understanding 3A and 3B, p. 34

Ex. 4: Solve | 2x – 5 | > 3. Graph the solution.

2x – 5 > 3 2x – 5 < -3

+5 +5

2x > 8

x > 4

+5 +5

2x < 2

x < 1

Solve check understanding 4 p. 35

Ex. 5: Solve -2| x + 1 | + 5 > -3

-2| x + 1| + 5 > -3

-5 -5

-2| x + 1| > -8

| x + 1| < 4

Ex. 5 cont.

x + 1 < 4 x + 1 > -4

-1 -1

x < 3

-1 -1

x > -5

Solve check understanding 5 p. 35

Ex. 6: The area A in square inches of a square photo is required to satisfy 8.5 < A < 8.9. Write

this requirement as an absolute value inequality.

Find the tolerance. 8.9 8.5 .4.2

2 2

8.5 8.9 17.48.7

2 2

Find the average of the maximum and

minimum values

Write the inequality -.2 < A – 8.7 < .2

Rewrite as an absolute value inequality | A – 8.7 | < .2

Homework

p. 36 – 37 # 1 – 53 eoo