Question

Solve the inequation given below. Write the solution set and represent it on the number line:

1 ≥ 15 – 7x > 2х – 27, x ∈ N

Answer 1

Given,

⇒ 1 ≥ 15 – 7x > 2x – 27

Solving L.H.S. of the inequation,

⇒ 1 ≥ 15 – 7x

⇒ 7x ≥ –1 + 15

⇒ 7x ≥ 14

⇒ `x ≥ (-14)/7`

⇒ x ≥ 2   ...(1)

Solving R.H.S. of the inequation,

⇒ 15 – 7x > 2x – 27

⇒ 2x – 27 < 15 – 7x

⇒ 2x + 7x < 15 + 27

⇒ 9x < 42

⇒ `x < 42/9`

⇒ `x < 4 6/9`   ...(2)

From (1) and (2) we get,

`2 ≤ x < 4 6/9`

Since, x ∈ N

Hence, solution set = {2, 3, 4}.

Solution on the number line is: