Solving Absolute Value Inequalities

Solving Absolute Value

Inequalities

2.6 Day 2

Learning Target:

Student will be able to…

●Solve absolute value inequalities with “OR” statement.

●Use absolute value inequalities to solve real-life problems.

Multiple Choice

Solve: $$\left|9+x\right|<4$$

• $$-5>x>-13$$

• $$-13<x<-5$$

• $$-13>x>-5$$

• No solution

Multiple Choice

Solve: $$\left|-7x\right|\le49$$

• $$x\le7$$

• $$x\ge-7$$

• $$-7\le x\le7$$

• x = 0

Multiple Choice

Solve: $$\left|\frac{x}{4}\right|<1$$

• $$4<x<-4$$

• $$x>-4$$

• $$x>4$$

• $$-4<x<4$$

Multiple Choice

Solve: $$\left|x-6\right|<2$$

• $$4<x<8$$

• x = -6
• x = 6 or x = -6
• x = 0

Example 1: Solving Absolute Value Inequalities

a)

|y+2| > 3

b)

|4x+7|+ 8 ≥ 17

c)

d)

Example 2: Solve the absolute value inequality.

Example 4: Special Cases

a)

|5p+2| < –4

b) |10-m| ≥ –2

c) |8x–11| < 0

Example 4

The menu at Jeanne’s favorite restaurant states that the roasted chicken with
vegetables entree typically contains 480 Calories. Based on the size of the
chicken, the actual number of Calories in the entree can vary by as many as 40
Calories from this amount.

a)

Write an absolute value inequality to represent the situation.

b)

What is the range of the number of Calories in the chicken entree?

Multiple Choice

Solve: $$\left|x-1\right|\ge5$$

• $$-4\ge x\ge6$$

• $$No\ Solution$$

• All Real Numbers