Xavier Aptitude Test 2014 Paper

(b) |x + 7| + |x – 8| = 16
Put x + 7 = 0 ⇒ x = – 7
Also put x – 8 = 0 ⇒ x = 8
Case-I: When x ≤ – 7, then
|x + 7| + |x – 8| = 16
⇒ – x – 7 – x + 8 = 16
⇒ x = – 7.5
Case-II: When – 7 < x < 8, then
|x + 7| + |x – 8| = 16
⇒ x + 7 – x + 8 = 16
⇒ 15 = 16, which is not possible
Case-III: When x ≥ 8, then
|x + 7| + |x – 8| = 16
⇒ x + 7 + x – 8 = 16
⇒ x = 8.5
Hence sum of the possible value of x = – 7.5 + 8.5 = 1