Solving Absolute Value Equations and Inequalities

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

Tags

CCSS.6.NS.C.7

CCSS.6.NS.C.8

Evaluate each expression.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

Tags

CCSS.8.EE.C.7

∣ 2x + 9 ∣ = 15

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

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

|−4 + 5x| = 16

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

Tags

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3

−2|−2r − 4| = -12

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

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

|v + 8| − 5 = 2 

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

Tags

CCSS.6.EE.B.5

CCSS.6.NS.C.7

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5
• x ≤ -2 OR x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x < 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Write an inequality for Graph 4.

• -2 < x < 5
• x < -2 or x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x ≤ 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

| 2w - 1 | < 11

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

| n + 2 | - 3 ≥ -6

• No Solution
• All Real Numbers
• n ≤ -5  or  n ≥ 1
• -5 ≤ n ≤ 1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3