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
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-> 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
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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.
