Solution
Expression : $$|x + 7| + |x - 8| = 16$$
Case 1 : $$x < -7$$
=> $$-(x + 7) - (x - 8) = 16$$
=> $$-2x + 1 = 16$$
=> $$x = \frac{-15}{2} = - 7.5$$
Case 2 : $$-7 \leq x < 8$$
=> $$(x + 7) - (x - 8) = 16$$
=> $$15 = 16$$, which is not possible.
Case 3 : $$x \geq 8$$
=> $$(x + 7) + (x - 8) = 16$$
=> $$2x - 1 = 16$$
=> $$x = \frac{17}{2} = 8.5$$
$$\therefore$$ Sum of all possible values of $$x = 8.5 - 7.5 = 1$$
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