The range of values of x which satisfy the inequality -2 x 2/3 ≤ x +1/3 < 3 x 1/3 : x ∈ R is

Question

The range of values of x which satisfy the inequality \(-2\frac23≤x + \frac13<3\frac13\) : \(x\) ∈ R is

(a) – 3 < x < 3 

(b) – 3 < x < 3 

(c) – ∞ < x < 3 

(d) 3 < x < ∞

Answer 1

(b) – 3 < x < 3

\(-2\frac23≤x + \frac13<3\frac13\) ⇒ \(\frac{-8}{3}≤x+\frac13<\frac{10}{3}\)

⇒ \(\frac{-8}{3}-\frac13≤x<\frac{10}{3}-\frac13\)

⇒ \(\frac{-9}{3}≤x<\frac93\) ⇒ – 3 < x < 3.