Solving Absolute Value Inequalities and Understanding Transformations

Solve the following inequality:

| x − 2 | > 3

• 2 < x < 10

• x < 2 or x > 10

• −1 < x < 5

• x < −1 or x > 5

Solve the following inequality:

| x + 1 | ≥ 3

• No Solution

• All Real Numbers

• x ≤ −4 or x ≥ 2

• −4 ≤ x ≤ 2

Solve the following inequality:

|10 + 4x| < 14

• x < 1 and x > −6

• x < 1 or x > −6

• x < 6 and x > −6

• x < 1 or x > −1

Solve the following inequality:

|3x + 6| ≥ 15

• x ≥ 3 or x ≤ −3

• x ≤ 7 and x ≤ −3

• x ≥ 7 and x ≤ −7

• x ≤ −7 or x ≥ 3

Show the missing steps for each side of the absolute value function

a

b

What is the correct first step?

(a)  

• divide by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and

• multiply by 10

Solve the following inequality:

|2x + 13| < 15

• x < 1 and x > −14

• x < 1 or x > −14

• x > 1 and x < −14

• x < 2 and x > −28

Solve the following inequality:

| 2w − 1 | < 11

• No Solution

• All Real Numbers

• −5 < w < 6

• −6 < w < 5

Solve the following inequality:

|x + 3| > − 8

• x > 5 or x < −11

• x > 5

• all real numbers

• no solution

Solve the following inequality:

|x + 4| − 8 > 2

• x > 6 and x < 10

• x > 6 or x < −14

• all real numbers

• no solution