A1-U1.7 Lesson: Absolute Value Inequalities

Open Ended

ACT Prep Question:

Describe the solutions to: $$\left|n+7\right|=11$$

Multiple Choice

ACT Prep Question:

How many solutions does the following equation have?
$$\left|n+7\right|=11$$

• 1

• 2

• None

• All Real

Multiple Select

ACT Prep Question:

Select the solution/s to:
$$\left|n+7\right|=11$$

• 4

• -18

• 0

• 18

• -4

Unit 1 Lesson 7b:
Absolute Value Inequalities

Goal:

Solve and graph absolute value inequalities, and solve real world problems of absolute value inequalities.

Procedures:

1) Isolate the absolute value.
2) Drop the absolute value bars.
3) Create a second inequality w/ the opposite output, and reverse the inequality sign.
4) Isolate the variables.
5) Graph the result.

Reorder

Reorder the following procedures used to solve problems of absolute value inequalities.

• Isolate the absolute value.

• Drop the absolute value bars.

• Create a second inequality w/ the opposite output, and reverse the inequality sign.

• Isolate the variables.

• Graph the result.

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Example 1:

Example 2:

Example 3:

Example 4:

Solve and explain:
Maria is training for a marathon and wants to maintain a consistent weekly running distance. She can tolerate a variation of up to 5 miles from her target distance of 40 miles per week.

1. Set up an absolute value inequality to represent the range of her acceptable weekly running distance.

2. Solve the inequality to find the minimum and maximum distances Maria should run each week.

 

Multiple Choice

Every time that you write the second absolute value inequality with the opposite output, you must also do what?

• Reverse the inequality sign.

• Rationalize the denominator.

• Take the square root of both sides.

• Prime factor the output.