SOLUTION: the absolute value of 7x-1/6= the absolute value of 6x+7/7 Solve the equation for x. List all the possible solutions.

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Question 780043: the absolute value of 7x-1/6= the absolute value of 6x+7/7
Solve the equation for x. List all the possible solutions.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
the absolute value of 7x-1/6= the absolute value of 6x+7/7
Solve the equation for x. List all the possible solutions.
***
|7x-1/6|=|6x+7/7|
Solve for 2 cases:
case 1:
7x-1/6=6x+7/7
x=1+1/6=
x=7/6
..
case 2:
7x-1/6=-(6x+7/7)
7x-1/6=-6x-1
13x=-1+1/6=-5/6
x=-5/78
..
Check:
for x=7/6
|7x-1/6|=|6x+7/7|
|(49/6)-1/6|=|6(7/6)+7/7|
|48/6|=|7+1|
8=8
check ok
..
for -5/78
|7x-1/6|=|6x+7/7|
|7(-5/78)-1/6|=|6(-5/78)+7/7|
|-35/78)-1/6|=|-30/78)+7/7|
|-35/78)-1/6|=|-30/78)+7/7|
|-0.615385...|=|0.615385...|
0.615385...=0.615385...
Check ok