Solving Absolute Value Equations with Extraneous 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

| 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"

−2|−2r − 4| = -12

• {5,1}

• {-5, -1}

• {-5, 1}

• No Solution

Match the following

• x = 5, -5

• 2|x| = 2

• x = -3, 1

• No Solution

• |x| = 5

• x = -20, 20

• -3 | x + 1 | = -6

• x = 1, -1

• |2x| = -2

|−4 + 5x| = 16

• {16/5,12/5}

• {4,-5}

• {-12/5, 4}

• 4

|v + 8| − 5 = 2 

• {-1,-15}

• {-1,-5}

• {-15,15}

• No Solution

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

Solve and check for extraneous solutions. 2|x + 5| - 6 = 8

• No Solution

• x  = 12 and x = -2

• x = -12 and x = 2

• x = -12

|2a - 10| = 6

• a = 8, a = 5

• a = 2

• a = 8

• a = 8, a = 2