SOLUTION: |x-7| = X+5

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Question 847439: |x-7| = X+5
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
|x-7| = X+5
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x-7 = x+5 or x-7 = -(x+5)
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x-7 = x+5 as a contradiction so has no solution.
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x-7 = -(x+5)
x-7 = -x-5
2x = 2
x = 1
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Cheers,
Stan H.
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Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The capital X must be a misprint. You must mean |x-7|=x+5.

An important restriction is that x%3E=-5, otherwise the statement becomes meaningless. Absolute value is always positive or zero.

With that restriction recognized, x-7 may still be either positive or negative or zero. Account for two conditions: x-7%3C0 and x-7%3E=0. Solve the equation according to each of those conditions, separately. Combine the solution parts appropriately.

The argument positive or zero:
x-7=x%2B5, with the restriction if needed, that x%3E=-5.
Solve for x.

The argument negative:
-x%2B7=x%2B5, with the restriction if needed, that x%3E=-5.
Solve for x.

I have left out the final solution steps, so you can enjoy the opportunity to continue the process.