Question

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

–5(x – 9) ≥ 17 – 9x > x + 2, x ∈ R

Answer 1

Given,

⇒ –5(x – 9) ≥ 17 – 9x > x + 2

Solving L.H.S. of the inequation,

⇒ –5(x – 9) ≥ 17 – 9x

⇒ –5x + 45 ≥ 17 – 9x

⇒ –5x + 9x ≥ 17 – 45

⇒ 4x ≥ 17 – 45

⇒ 4x ≥ –28

⇒ `x ≥ - 28/4`

⇒ x ≥ –7   ...(1)

Solving R.H.S. of the inequation,

⇒ 17 – 9x > x + 2

⇒ x + 2 < 17 – 9x

⇒ x + 9x < 17 – 2

⇒ 10x < 15

⇒ `x < 15/10`

⇒ `x < 3/2`   ...(2)

From (1) and (2) we get,

⇒ `-7 ≤ x < 3/2`

Since, x ∈ R

Hence, solution set = `{x : -7 ≤ x < 3/2, x ∈ R}`

Solution on the number line is: