Absolute Value Equations and Inequalities

Solve.

|x + 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

Solve.

3|d - 4| ≥ 12

• d = -8 or d = 0

• no solution

• d ≥ 8 or d ≤ 0

• d = 40 or d = 32

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve:
|x + 3| > - 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve:  |2x + 1| ≤ 19

• x ≥ 9 or x ≤ -10

• -10 ≤ x ≤ 9

• x ≥ 10 or x ≤ -9

• -9 ≤ x ≤ 10

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Solve for x
l 4x−3 l = 17

• x = 5 and x =-3.5
• x = 0 and x = -5
• x = 10 and x = -10
• No Solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

Solve for x
l x−6 l + 4= 10

• x = 12 and x = 0
• x = 3 and x = -3
• x = -12 and x = 0
• No Solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.REI.A.1

Evaluate each expression.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

Tags

CCSS.HSA.REI.A.1