SOLUTION: I have another absolute value problem that is stumping me. We are supposed to solve for x: |3x| = |x-1| + 2 . Thank you for your help. welljesse

Question 59575: I have another absolute value problem that is stumping me. We are supposed to solve for x:
|3x| = |x-1| + 2 .
Thank you for your help.
welljesse
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I have another absolute value problem that is stumping me. We are supposed to solve for x:
|3x| = |x-1| + 2 .
CASE 1 ....X-1>0....OR....X>1
|3X|=3X...AS OBVIOUSLY X>0.....|X-1|=X-1
3X=X-1+2=X+1
2X=1
X=1/2....THIS DOES NOT SATISFY THE ASSUMPTION AT THE BEGINING THAT X>1
HENCE NOT POSSIBLE
CASE 2....X-1<0....X<1....BUT 3X>0....OR...X>0
|3X|=3X....|X-1|=-(X-1)=-X+1
3X=-X+1+2
4X=3
X=3/4..THIS SATISFIES THE ASSUMPTION AT THE BEGINING THAT X<1 AND X>0
HENCE THIS IS ONE POSSIBLE SOLUTION.
CASE 3 .....3X<0.....X<0....
|3X|=-3X.........|X-1|=-(X-1)=-X+1.....AS OBVIOUSLY X<1
-3X=-X+1+2=-X+3
-2X=3
X=-3/2...THIS SATISFIES THE ASSUMPTION AT THE BEGINING THAT X<0
HENCE THIS IS A POSSIBLE SECOND SOLUTION.

Thank you for your help.
welljesse

RELATED QUESTIONS
We are supposed to solve for x. The problem is: 1/x(squared) - 7x + 10 = x/x-5 + 1/x -... (answered by scott8148)

I have a problem that is stumping me. I would appreciate your help very much! The problem (answered by tutorcecilia)

if you could can you please explain to me how to solve this math problem? thank you soooo (answered by Theo)

I need to graph this absolute value function: t(x) = 3- the absolute value x.(I don't... (answered by stanbon)

Solve the absolute value equation. Solve |x + |3x-2|| = 2 Note: Here we have... (answered by math_tutor2020,greenestamps)

okay... :) I am in 8th grade and curently takeing Algebra 1. We are working on solveing... (answered by Alan3354)

Please help me solve. Thank you (1-x)^2=9 I think that I am supposed to set it to... (answered by checkley77)

Please help me solve. Thank you (1-x)^2=9 I think that I am supposed to set it to... (answered by checkley77,jsmallt9)

Not sure how to solve Absolute Value Equations that have fraction. Example: Solve... (answered by solver91311)