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
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