INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### Inequalities with Absolute Values

• To solve an inequality involving absolute value, convert the original inequality into a compound inequality that does not involve absolute value, using the definition of absolute value. For example, |2x + 3| > 4 would become: either 2x + 3 > 4 or 2x + 3 < -4.
• Describe the solution set of a compound inequality using either a number line or set builder notation.

### Inequalities with Absolute Values

Solve | b − 6 |≥ 7
• b − 6 ≥ 7 b − 6 ≤ − 7
• b − 6 ≥ 7
• b ≥ 13
• b − 6 ≤ − 7
• b ≤ − 1
b ≥ 13 and b ≤ − 1
| 5a − 2 |< 18
• 5a − 2 < 185a − 2 >− 18
• 5a − 2 < 18
• 5a < 20
• a < 4
• 5a − 2 >− 18
• 5a >− 16
• a >− [16/5]
• a > - 3[1/5]
a < 4 and a >− 3[1/5]
− 3[1/5] < a < 4
| w − 3 |≤ 18
• w − 3 ≤ 18
w − 3 ≥ − 18
• w − 3 ≤ 18
• w ≤ 21
• w − 3 ≥ − 18
• w ≥ − 15
w ≤ 21 and w ≥ − 15
− 15 ≤ w ≤ 21
| f − 8 |< 17
• f − 8 < 17f − 8 >− 17
• f − 8 < 17
• f < 25
• f − 8 >− 17
• f >− 9
f < 25 and f >− 9
− 9 < f < 25
| m + 7 |> 1
• m + 7 > 1m + 7 <− 1
• m + 7 > 1
• m >− 6
• m + 7 <− 1
• m <− 8
m >− 6 and m <− 8
| r + 10 |≤ 3
• r + 10 ≤ 3r + 10 ≥ − 3
• r + 10 ≤ 3
• r ≤ − 7
• r + 10 ≥ − 3
• r ≥ − 13
r ≤ − 7 and r ≥ − 13
− 13 ≤ r ≤ − 7
| y + 16 |< 49
• y + 16 < 49y + 16 >− 49
• y + 16 < 49
• y < 33
• y + 16 >− 49
• y >− 65
y < 33 and y >− 65
− 65 < y < 33
| 2d − 6 |> 10
• 2d − 6 > 102d − 6 <− 10
• 2d − 6 > 10
• 2d > 16
• d > 8
• 2d − 6 <− 10
• 2d <− 4
• d <− 2
d > 8 and d <− 2
| 4x − 3 |> 13
• 4x − 3 > 134x − 3 <− 13
• 4x − 3 > 13
• 4x > 16
• x > 4
• 4x − 3 <− 13
• 4x < 10
• x < [10/4]
• x < 2[2/5]
x > 4 and x < 2[2/5]
| 5m − 10 |> 35
• 5m − 10 > 355m − 10 <− 35
• 5m − 10 > 35
• 5m > 45
• m > 9
• 5m − 10 <− 35
• 5m < 25
• m < 5
m > 9 and m < 5

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Inequalities with Absolute Values

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Inequalities of the Form |x|< n 0:07
• Values that Satisfy Both Inequalities
• Example
• Inequalities of the Form |x|> n 3:58
• Values that Satisfy Either Inequalities
• Example
• Example 1: Solve the Inequality 6:38
• Example 2: Solve the Inequality 9:54
• Example 3: Solve the Inequality 12:05
• Example 4: Solve the Inequality 14:50