Absolute Value Inequalities

Which statement best describes l -4 l?

• the distance from -4 to 4 on a number line

• the distance from 4 to 0 on a number line

• the distance from -4 to 0 on a number line

• the distance from 0 to 4 on a number line

Tags

CCSS.6.NS.C.6

CCSS.6.NS.C.7

Solve.
|c + 4| < 5

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|y - 4| ≥ 8

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|y - 1| ≤ 6

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|p + 3| ≥ 10

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.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.CED.A.1

CCSS.HSA.REI.B.3

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.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|4k + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5
• -4.5 ≤ v ≤ -1.4
• -1.5 ≤ v ≤ 4.5
• v ≤ -1.5 or v ≥ 4.5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
3|2d + 9| + 13 = 10

• d = 5 or d = -1
• d = -4 or d = 5 
• d = 4 or d = -5
• no solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3