Absolute Value Inequalities

|-9v| < 54

• -6<v<6
• v<-6 or v>6
• v=6 or v=-6
• -6>v<6

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:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Solve.
-5|x - 4| > -20

• x < 8 and x > 0
• x > 8 or x < 0
• all real numbers
• no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Solve.
|2t + ⅔| < 4

• -5/3 < t < 7/3
• t > 7/3 or t < -5/3
• -7/3 < t < 5/3
• t > 5/3 or t < -7/3

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

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

• all real numbers
• no solution
• 0 < v < 6⁄7
• 0 ≤ v ≤ 6/7

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

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

A golf ball manufacturer puts 390 golf balls in each box. The box can be off by 6 golf balls. Write an inequality that displays the acceptable amount of golf balls that can be in a box.

• |x - 6| < 390

• |x - 6| ≤ 390

• |x - 390| < 6

• |x - 390| ≤ 6

Tags

CCSS.6.NS.C.7C