Answer:
To find the expressions without absolute values, we'll consider the given range of values for 'x' (-5 ≤ x ≤ 2) and evaluate the expressions accordingly:
A = |x + 5| + |x - 2|
For -5 ≤ x ≤ 2:
When x is between -5 and 2, the expression |x + 5| evaluates to -(x + 5) since x + 5 is negative within this range.
Similarly, |x - 2| evaluates to (x - 2) since x - 2 is positive within this range.
So, A = -(x + 5) + (x - 2) = -x - 5 + x - 2 = -7.
B = |x + 7| - |x + 15|
For -5 ≤ x ≤ 2:
When x is between -5 and 2, both expressions |x + 7| and |x + 15| evaluate to (x + 7) and (x + 15) respectively, since x + 7 and x + 15 are both positive within this range.
So, B = (x + 7) - (x + 15) = x + 7 - x - 15 = -8.
C = |3 - x| + |5 - x|
For -5 ≤ x ≤ 2: When x is between -5 and 2, both expressions |3 - x| and |5 - x| evaluate to (3 - x) and (5 - x) respectively, since 3 - x and 5 - x are both positive within this range.
So, C = (3 - x) + (5 - x) = 8 - 2x.
Therefore, the expressions without absolute values are:
A = -7
B = -8
C = 8 - 2x.