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Rewrite each equation without absolute value for the given conditions. y=|x-3|+|x+2|-|x-5| if -2

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MrRoyalidn

The equation y = |x-3| + |x+2| - |x-5| is an absolute value equation

The equivalent equation of y = |x-3| + |x+2| - |x-5|  if -2 < x < 3 is y = x

How to rewrite the absolute value equation?

The equation is given as:

y = |x-3| + |x+2| - |x-5|

The condition is given as:

if -2 < x < 3

Split and solve each term of the absolute value equation.

|x-3| = -(x - 3) = 3 - x....... because x < 3

|x+2| = x + 2 because -2 < x

|x-5| = -(x - 5) = 5 - x....... because x < 5

So, we have:

y = |x-3| + |x+2| - |x-5|

This gives

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

Open the brackets

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

Evaluate the like terms

y = x

Hence, the equivalent equation of y = |x-3| + |x+2| - |x-5|  if -2 < x < 3 is y = x

Read more about absolute value equations at:

https://brainly.com/question/12344256

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