Answer :
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