Absolute Value Equations and Extraneous Solutions

Solve |2x –3| + 5 =10.

Select all of the valid solutions,

do not select if the solution is extraneous

• –1

• 4

• 1

• –4

• 2

solve:

3| −8x| + 8 = 80

• {−7/3, 7/3}

• {−3,3}

• {11/3,−11/3}

• No Solution

solve: |−2n| + 10 = −50

• {30, −30}

• {20,−20}

• {−5,5}

• No Solution

Solve.

4| x + 9 | = 20

Select all of the valid solutions,

do not select if the solution is extraneous

• x = −14

• x = −4

• x = 4

• x = 14

• x = −3

solve

|−2n| + 10 = 50

Select all of the valid solutions,

do not select if the solution is extraneous

• n = 20

• n = −20

• n = −5

• No Solution

• n = 5

Solve

|x – 12| − 3 = 11

Select all of the valid solutions,

do not select if the solution is extraneous

• −2

• 26

• 3

• 4

• 2

solve: 2|x – 12| − 6 = 22

• −2, −26

• −2, 26

• 3, 25

• 4, −7

solve: 3|v + 8| − 15 = 6

• {−1,−15}

• {−1,−5}

• {−15,15}

• No Solution

solve: |2a − 10| = 6

Select all of the valid solutions,

do not select if the solution is extraneous

• a = 5

• a = 2

• a = 8

• a = −8

• no solution

Solve:

9|9 − 2p| = 81

• p = 0, p = −9

• p = −63/2, p = 99/2

• p = 0, p = 9

• No Solution