The sum of the possible values of X in the equation |X + 7| + |X – 8| = 16 is:
Explanation:
|X + 7| + |X – 8| = 16 For X ≥ 8, |X + 7| = X + 7 and |X – 8| = X – 8 ∴ |X – 7| + |X – 8| = X + 7 + X – 8 = 2X – 1 2X – 1 = 16
∴X=172
For -7 ≤ x < 8, ∴ |X + 7| = X + 7 & |X – 8| = 8 – X ∴ |X + 7| = |X – 8| = X + 7 + 8 – X = 15 ≠ RHS 0 ≤ x < 8 is not possible. -7 ≤ x < 0 ∴ |X + 7| = 7 + X & |X – 8| = -X + 8 16 = |X + 7| + |X – 8| = 7 + X – X + 8 = 15 ∴ -7 ≤ x < 0 is not possible. Now, x < -8 |X + 7| = - 7 – x |X – 8| = -X + 8 ∴ |X + 7| + |X – 8| = - 7 – X – X + 8 = 1 – 2X = 16 ⇒ 2X = -15 ⇒ X = -7.5 Hence, option (b).
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