Solving Multi-Step Absolute Value Equations and Inequalities

Algebraic statements that have <, >, ≤, ≥, or ≠ as their symbols of comparison.

• Inequalities

• Equations

• Variables

• Coefficients

Algebraic equations that require more than one operation to solve.

• Distributing

• Multi-Step Equations

• Expressions

• Variables

We see these symbols with an:

• Inequality

• Equation

• Expression

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

Review the work shown solving the inequality. Should the inequality symbol been reversed?

• Yes, because 2 is positive.

• ​No, because 2 is positive.

• ​Yes, because −4 is negative.

• No, because −4 is negative.

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

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:

| 2w − 1 | < 11

• No Solution

• All Real Numbers

• −5 < w < 6

• −6 < w < 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:

|x + 3| > − 8

• x > 5 or x < −11

• x > 5

• all real numbers

• no solution