Find the set of values of x satisfying |(5-x)/3|< 2

Question

Find the set of values of x satisfying \(\bigg|\frac{5-x}{3}\bigg|<2\)

(a) 1 < x < 11 

(b) – 1 < x < 11 

(c) x < 11 

(d) None of these

Answer 1

(b) –1 < x < 11

\(\bigg|\frac{5-x}{3}\bigg|<2\)  ⇒ |5-x| < 6

⇒ – 6 < 5 – x < 6 ⇒ –11 < – x < 1 ⇒ 11 > x > – 11 

(∵ a < b < c ⇒ ma > mb > mc, when m is –ve. Here m = –1) 

⇒ –1 < x < 11.