1.4 Solving Absolute Value Equations

An absolute value equation is

• an equation that contains an absolute value expression
• always going to have two solutions
• always going to have one solution
• impossible to solve

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.D.11

|a| ≥ 0

• The absolute value of a number is always negative
• The absolute value of a number is always positive or zero

| x + 6 | = 11

• x = -6 and x = 11
• No Solution
• x = 5 and x = -17
• x = -5 and x = 17

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

| 2x - 1 | = -4

• x = ¹/₂ and x = -4
• No Solution
• x = ^-3/₂ and x = ⁵/₂
• x = ³/₂ and x = ^-5/₂

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

| 3x - 6 | - 9 = -3

• No Solution
• x = 0 and x = 4
• x = 2 and x = -2
• x = -4 and x = 4

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

| 3n + 12 | = 2n

• No Solution
• n = -12 and n = ^-12/₅
• n = -12
• n = ^-12/₅

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.A.2

What are the two related linear equations for solving:
| x - 4 | = 8

• x - 4 = 8 and x + 4 = 8
• x - 4 = 8 and x - 4 = -8

Tags

CCSS.HSA.REI.B.3

An extraneous solution is

• not a concern when solving absolute value equations
• an apparent solution that must be rejected because it does not satisfy the original equation

Tags

CCSS.HSA.REI.A.2