Absolute Value Inequalities

|v| < 5

• -5<v<5

• v<-5 or v>5

• v<-5 and v<5

• -5>v<5

Solve:

|x| > 8

• x > 8 or x < -8

• -8<x<8

• x>-8 or x>8

• x > 8 and x < -8

|p+4|≤ 8

• -42 ≤ p ≤ 16
• -5 ≤ p <6
• 12 > p > 9
• -12 ≤ p ≤ 4 

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

|r|-3 >2

• |r|+6 <-6
• |r|-3 >2
• |r|-37≤ 2
• r>5 or r<-5

|b-8|+10>22

• -4<b<20
• b<-4 or b>20
• 20<b<-4
• b=-4 or b=20

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.3

CCSS.HSA.REI.A.1

4|5x-2|+7>39

• -6/5<x>2
• x=2 or x=-6/5
• x=2 and x=-6/5
• x<-6/5 or x>2

Tags

CCSS.6.NS.C.7C

• v>5 or v<-5
• v≥5 or v≤-5
• v>-5 or v<5
• all real numbers

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

| 2w - 1 | < 11

• No Solution
• All Real Numbers
• -5 < w < 6
• -6 < w < 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.3

3 | 2t - 3 | - 5 > 16

• No Solution
• All Real Numbers
• t < -2  or  t > 5
• -2 < t < 5

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

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