SOLUTION: How do you solve y=|x-3|+|x+2|-|x-5|, if 3 is less than x which is less than 5?

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Question 1073178: How do you solve y=|x-3|+|x+2|-|x-5|, if 3 is less than x which is less than 5?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
If the required interval on x is used, then abs%28x-3%29 will be non-negative, and abs%28x-5%29 may be either negative or 0. All values of the required interval will make abs%28x%2B2%29 to be positive.

The equation in the expected, given interval becomes

y=%28x-3%29%2Bx%2B2%2Bx-5
OR
y=%28x-3%29%2Bx%2B2-%28x-5%29

Simplifying those system%28y=3x-6%2COR%2Cy=x%2B4%29.

Only ONE value of x will use the second equation, x at 5.
The rest of the x values will use the first equation, y=3x-6.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

How do you solve y=|x-3|+|x+2|-|x-5|, if 3 is less than x which is less than 5?
3 < x < 5

If x takes on an INTEGER value, then x MUST BE 4.

Hence, y = 6