Solving Absolute Value Equations and Inequalities

| x + 3 | ≤ 2

• No Solution

• All Real Numbers

• -5 ≤ x ≤ -1

• 1 ≤ x ≤ 5

| 3c - 5 | < -2

• No Solution

• All Real Numbers

• 1 < c < ⁷/₃

• c < 1 or c > ⁷/₃

|b-8|+10>22

• -4<b<20

• b<-4 or b>20

• 20<b<-4

• b=-4 or b=20

 Solve:
|−2n| + 10 = −50

• {30, -30}

• {20,-20}

• {-5,5}

• No Solution

5x|-1>-11

• - 1< x > 1

• x=2 or x=-1

• x=1 and x=-1

• x < -1 or x > 1

|−4 + 5x| = 16

• {16/5,12/5}

• {4,-5}

• {-12/5, 4}

• 4

−2|−2r − 4| = -12

• {5,1}

• {-5, -1}

• {-5, 1}

• No Solution

∣ 2x + 9 ∣ = 15

• x = 3 

• x = 3
  x = -6

• x = 3
  x = -12

• x = 6
  x = -12

Solve |x – 12| - 3 = 11.

• -2, -26

• -2, 26

• 3, 25

• 4, -7

• x > 11 or x < 5
• x > - 11 or x > 5
• 5 < x < 11
• - 5 < x < 11