SOLUTION: Solve the equation and write the solution set. Show your work. |3x-5|+2=5x-1

Algebra ->  Absolute-value -> SOLUTION: Solve the equation and write the solution set. Show your work. |3x-5|+2=5x-1      Log On


   

Question 908845: Solve the equation and write the solution set. Show your work.
|3x-5|+2=5x-1
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
|3x-5|+2=5x-1
abs%283x-5%29=5x-1-2
abs%283x-5%29=5x-3

CASE, 3x-5 positive or zero.
3x-5=5x-3
3x-5x-5=-3
-2x-5=-3
-2x=-3%2B5
-2x=2
highlight%28x=-1%29

CASE, 3x-5 NEGATIVE.
-3x%2B5=5x-3
-3x-5x%2B5=-3
-8x%2B5=-3
8x-5=3
8x=3%2B5
8x=8
highlight%28x=1%29

SOLUTION: highlight%28x=-1%29 OR highlight%28x=1%29, ... but these do not work.

CHECK SOLUTION:
-------------------------------
|3x-5|+2=5x-1
abs%283%28-1%29-5%29%2B2=5%28-1%29-1
8%2B2=-6
10=-6, clearly FALSE.
-
abs%283%2A1-5%29%2B2=5%2A1-1
abs%28-2%29%2B2=4, clearly FALSE.
2%2B2=4, TRUE.

RESULT: -1 fails; but +1 works.
ANSWER: highlight%28x=1%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
answer is +1
and it works
|3x-5|+2=5x-1
|3(1)-5|+2=5(1)-1
4=4