U6L3 Absolute Value Inequalities

| x - 6 | < 4
Is this an "and"  or an "or" problem?

• and
• or

| 2x + 12 | < 8
Which is the correct first step?

• 2x + 12 < 8 and 2x+12 >-8
• 2x + 12 < 8 or 2x+12 >-8
• 2x + 12 < 8 and 2x+12 <-8
• 2x + 12 < 8 or 2x+12 >-8

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and
• or

What is the first step? 

• Get absolute value alone by subtracting 5 from both sides
• Get absolute value alone by dividing by 5 on both sides
• Split into two equations

Solve.

|x + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

Solve.
|3c - 4| < 12

• -2 2/3 < c < 5 1/3
• c < -5 1/3  or c > 2 2/3
• c < 5 1/3 or c > -2 2/3
• -5 1/3 < c < 2 2/3

Solve.
|5x + 7| < 22

• x < -5 ⅘ or x > 3
• -5 ⅘ < x < 3
• -3 < x < 5 ⅘
• x < -3 or x > 5 ⅘

Solve.

3|2d + 9| + 13 > 10

• d > 5 or d < -1

• d < -4 or d > 5

• No Solution

• All real numbers

Solve.
|4m + 9| ≥ 21

• -7.5 ≤ m ≤ 3
• m ≤ -7.5 or m ≥ 3
• -3 ≤ m ≤ 7.5
• m ≤ -3 or m ≥ 7.5