Solving Absolute Value Equations and Inequalities

|v + 8| − 5 = 2

• {-15,-1}

• {-1,-5}

• {-15,15}

• No Solution

|2a - 10| = 6

• a = 5

  a = 8

• a = 2

• a = 8

• a = 2

  a = 8

|−4 + 5x| = 16

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

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3

|2x + 9| = 15

• x = 3

• x = -6

  x = 3

• x = -12

  x = 3

• x = -12

  x = 6

|6 - 2k| = 18

• k = -6

• k = -6

  k = 12

• k = -12

  k = -6

• k = -6

  k = 5

|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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

| 3c - 5 | < -2

• No Solution
• All Real Numbers
• 1 < c < ⁷/₃
• c < 1  or  c > ⁷/₃

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

| x + 1 | ≥ 3

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

Tags

CCSS.6.NS.C.7C

−2|−2r − 4| = -12

• {5,1}

• {-5,-1}

• {-5,1}

• No Solution