Solving Linear and Absolute Value Equations and Inequalities

|v + 8| − 5 = 2 

• {-1,-15}
• {-1,-5}
• {-15,15}
• No Solution

|−4 + 5x| = 16

• {16/5,12/5}
• {4,-5}
• {-12/5, 4}
• 4

∣ 2x + 9 ∣ = 15

• x = 3 
• x = 3
  x = -6
• x = 3
  x = -12
• x = 6
  x = -12

|-2 - 4n| = 34

• n = -9, n = 8
• n = 9, n = 8
• n = -9
• n = 8

|6 - 2f| = -5

• 11/2, 1/2
• -5, 5
• 1, 3
• ⊘ No solution

| 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

| k - 3 | < -1

• No Solution
• All Real Numbers
• 2 < k < 4
• k < 2  or  k > 4

| x + 1 | ≥ 3

• No Solution
• All Real Numbers
• x ≤ -4  or  x ≥ 2
• -4 ≤ x ≤ 2

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution