Question

The sum of the possible values of X in the equation $|X + 7| + |X - 8| = 16$ is:

Accepted Answer

B. Case 1: $X < -7 \implies -(X+7) - (X-8) = 16 \implies -2X + 1 = 16 \implies X = -7.5$. Case 2: $-7 \le X < 8 \implies (X+7) - (X-8) = 16 \implies 15 = 16$ (No solution). Case 3: $X \ge 8 \implies (X+7) + (X-8) = 16 \implies 2X - 1 = 16 \implies X = 8.5$. Sum of possible values $= 8.5 - 7.5 = 1$.

Absolute Value Equation

Explanation

Practise this under exam conditions