Absolute Value Equations and Inequalities

Absolute Value Equations & Inequalities in One Variable

by Michelle Wilson

Multiple Choice

Solve the 2 cases

1) -2x - 5 = 1

2) -2x - 5 = 1

• x = 3 or 2

• x = -2 or -3

Multiple Choice

What are the 2 cases for |x - 8| = 16 ?

• x - 8 = 16

  or

  -x - 8 = -16

• x + 8 = 16

  or

  -x - 8 = -16

• x - 8 = 16

  or

  -x + 8 = 16

Multiple Choice

What are the 2 cases for |7x + 7| = 56 ?

• 7x - 7 = -56

  or

  -7x - 7 = 56

• 7x + 7 = 56

  or

  -7x - 7 = 56

• -7x + 7 = -56

  or

  7x - 7 = 56

Multiple Choice

What does 7|5x + 1| - 10 = -3

look like when you isolate the absolute value bars?

Note: "isolate" is another word for "get alone"

• 7|5x + 1| = -7

• |5x + 1| - 10 = 4

• |5x + 1| = -1

• |5x + 1| = 1

​When is there No Solution?

​Once the Absolute Value bars are alone, they must equal a positive number.

​

​|x - 4| = 5 has two solutions

​However,

|x - 4| = -5 has no solution

​

​The absolute value of something cannot equal a negative value (as shown in the example on this slide and the next).

Multiple Choice

Which equation has NO solution?

• |3x - 1| = 5

• |3x - 1| = 25

• |3x - 1| = -5

​Did you write the last slide down?

​Knowing when to use "and" or "or" for Absolute Value Inequalities is important!

Multiple Choice

Given: |x| > 4

What would the 2 cases be?

• x > 4 AND x < -4

• x > 4 OR x < -4

Multiple Choice

Given: |x| < 7

What would the 2 cases be?

• x > 7 AND x < -7

• x > 7 OR x < -7

Multiple Choice

What is the correct first step?

 |x + 3| > 8

• Set up two cases with "and"

• Set up two cases with "or"

• Subtract 3 from both sides

Multiple Choice

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and"

• separate into two inequalities with an "or"

• divide both sides by -8

Multiple Choice

What is the correct first step?

• divide by 10
• multiply by 10
• make it two inequalities with an "or"
• make it two inequalities with and "and

Poll

Tomorrow we practice this. How do you feel about that?

• Great! I have my notes/examples written down and will be fine.

• I may send you a Google Chat to ask some questions, but I will be okay.

• Not great. I will redo this Quizizz (take good notes) and watch some of the extra help videos you posted.