Mathematics

List the elements of the solution set of inequation -3 < x - 2 ≤ 9 - 2x; x ∈ N.

27 Likes

Given,

⇒ -3 < x - 2 ≤ 9 - 2x

Solving L.H.S. of the equation,

⇒ -3 < x - 2

⇒ x > -3 + 2

⇒ x > -1 …….(i)

Solving R.H.S. of the equation,

⇒ x - 2 ≤ 9 - 2x

⇒ x + 2x ≤ 9 + 2

⇒ 3x ≤ 11

⇒ x ≤ $\dfrac{11}{3}$ ………(ii)

From (i) and (ii) we get,

⇒ -1 < x ≤ $\dfrac{11}{3}$ .

Since, x ∈ N

∴ Solution set = {1, 2, 3}.

Answered By

16 Likes