Absolute Value Equations and Extraneous Solutions

| 2x + 12 | < 8

Which is the correct first step?

• 2x + 12 < 8 and 2x+12 > -8

• 2x + 12 < 8 or 2x+12 > -8

• 2x + 12 < 8 and 2x+12 < -8

• 2x + 12 < 8 or 2x+12 < -8

What is the correct first step?

• divide by 10

• multiply by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and"

4|5x-2|+7>39

• -6/5<x>2

• x=2 or x=-6/5

• x=2 and x=-6/5

• x<-6/5 or x>2

What is the solution of ∣5x-2∣=7x+14?

• x=-1

• x=-1, x=-8

• x=-8

• no solutions

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

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

|a| ≥ 0

• The absolute value of a number is always negative

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

| 3x - 6 | - 9 = -3

• No Solution

• x = 0 and x = 4

• x = 2 and x = -2

• x = -4 and x = 4

| 3n + 12 | = 2n

• No Solution

• n = -12 and n = ^-12/₅

• n = -12

• n = ^-12/₅

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