Respuesta :

samkr14

Answer:

x=3 is the extraneous solution

Step-by-step explanation:

|4x-42| = -10x

Since it's absolute value and we know that there are two possibilities, we need two equations to set up to solve for x.

1st equation:

  • 4x - 42 = -10x

2nd equation:

  • 4x - 42 = 10x

Solve both equations for x:

  • 1st equation:
  • 4x - 42 = -10x
  • 14x-42 = 0
  • 14x=42
  • x = 3
  • 2nd equation:
  • 4x-42=10x
  • -6x-42=0
  • -6x=42
  • x=-7

Plug in both values for x in the original equation to find the extraneous solution:

x=-7

  • |4x-42|=-10x
  • |4(-7)-42|=-10(-7)
  • |-28-42|=70
  • |-70|=70
  • 70=70

x=3

  • |4x-42|=-10x
  • |4(3)-42|=-10(3)
  • |-30|=-30
  • 30≠-30

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