Absolute Value Equations

• {-1, 16}

• {0,12}

• No Solution

• {5, 13}

• -2.771
• -1.433
• -1.9722
• -3.4777

• 0

• 1

• 2

• Infinitely Many

An extraneous solution is a solution that appears to be true but when you plug it into the equation you get a ​ (a)   solution.

• False
• True

Mathematical Equivalence

ON

• {-5, 17}

• No Solution

• {-1, 18}

• {-6, 10}

Groups:

(a) Is a Solution

,

(b) Is Extraneous

• no solution

• -5

• 5

• 0.1

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

• -14
• -4
• {-14, -4}
• no solution

∣ 2x + 9 ∣ = 15

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