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Rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if 3 is smaller than x which is smaller than 5. Sorry for reposting, there were some glitches. Please do not put links.

User Morio
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1 Answer

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Answer:

y = 3x -6

Explanation:

The three turning points of the terms divide the graph into 4 pieces. We can consider what functions apply in each piece.

x < -2

All terms are negated:

y = (3 -x) -(x +2) -(5 -x) = -x -4

-2 < x < 3

The first and last terms are negated:

y = (3 -x) +(x +2) +(x -5) = x

3 < x < 5

The last term is negated:

y = (x -3) +(x +2) +(x -5) = 3x -6

5 < x

No terms are negated:

y = (x -3) + (x +2) -(x -5) = x +4

_____

In the region of interest, the equation simplifies to y = 3x -6.

Rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if 3 is-example-1
User Mrvol
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