Final answer:
To rewrite the expression without absolute values given x > -2, consider each term's behavior within the given range. This results in y = (x-3) + (x+2) - (-(x-5)), which simplifies to y = 3x - 6.
Step-by-step explanation:
To rewrite the expression y = |x−3| + |x+2| − |x−5| without absolute values, given the condition that x > −2, we need to consider the behavior of each absolute value term separately within the given range.
Since x > −2, the expression |x+2| equals (x+2) because x+2 will be non-negative. The expression |x-3| becomes (x-3) because x is greater than 3 which makes x-3 positive. Finally, the expression |x-5| is rewritten as −(x-5) since x is less than 5, which makes x-5 negative within the range −2 < x < 5, and the absolute value negates that negative.
The expression without absolute values is: y = (x-3) + (x+2) - (-(x-5)). Simplifying the expression, we get:
y = x - 3 + x + 2 + x - 5
This simplifies to:
y = 3x - 6
Therefore, for x > −2, the simplified expression for y is y = 3x - 6.