SOLUTION: |4x-7|=5 |3-8x|=1 What value of x satisfies both of the equations above?

Algebra ->  Absolute-value -> SOLUTION: |4x-7|=5 |3-8x|=1 What value of x satisfies both of the equations above?      Log On


   

Question 665532: |4x-7|=5
|3-8x|=1
What value of x satisfies both of the equations above?
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
|4x-7|=5 has two solutions derived from 4x-7=5 and 4x-7=-5. Solving the first:
4x - 7 = 5
4x - 7 + 7 = 5 + 7
4x = 12
x = 3
Solving the second:
4x - 7 = -5
4x - 7 + 7 = -5 + 7
4x = 2
x = 1/2

Likewise, |3-8x|=1 also has two solutions derived from 3-8x=1 and 3-8x=-1. Solving the first:
3 - 8x = 1
3 - 8x - 3 = 1 - 3
-8x = -2
x = 1/4
Solving the second:
3 - 8x = -1
3 - 8x - 3 = -1 - 3
-8x = -4
x = 1/2

So x = 1/2 will make both equations true.