Question

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

5x – 11 ≤ 7x – 5 < 9, x ∈ R

Answer 1

Solving L.H.S. of the inequation,

⇒ 5x – 11 ≤ 7x – 5

⇒ 7x – 5 ≥ 5x – 11

⇒ 7x – 5x ≥ –11 + 5

⇒ 2x ≥ –6

⇒ `x ≥ - 6/2`

⇒ x ≥ –3   ...(1)

Solving R.H.S. of the inequation,

⇒ 7x – 5 < 9

⇒ 7x < 9 + 5

⇒ 7x < 14

⇒ `x < 14/7`

⇒ x < 2   ...(2)

From (1) and (2) we get,

–3 ≤ x < 2

Since, x ∈ R

Hence, solution set = {x : –3 ≤ x < 2, x ∈ R}.

Solution on the number line is: