absolute value inequalities

Solve.
|c + 4| < 5

• x < -9 or x > 1
• -9 < x < 1
• x < 9 or x > -1
• -1 < x < 9

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve.
|y - 4| ≥ 8

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

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5
• y ≤ -7 or y ≥ 5
• -5 ≤ y ≤ 7
• y ≤ -5 or y ≥ 7

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Solve.
|p + 3| ≥ 10

• -13 ≤ p ≤ 7
• p ≤ -13 or p ≥ 7
• -7 ≤ p ≤ 13
• p ≤ -7 or p ≥ 13

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

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

Tags

CCSS.HSA.REI.B.3

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

| 2w - 1 | < 11

• No Solution

• w < 5

• -5 < w and w < 6

• -6 < w and w < 5

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

| x + 3 | > 8

• No Solution
• All Real Numbers
• x < -11  or  x > 5
• -5 < x < 11

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

| -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

• add 8 to both sides

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve the absolute Value inequality and graph. 

• A
• B
• C
• D

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1