Question

Solve the following inequation. Write down the solution set and represent it on the real number line.

–5(x – 9) ≥ 17 – 9x > x + 2, x ∈ R

Answer 1

Given: –5(x – 9) ≥ 17 – 9x > x + 2, x ∈ R

`\implies` –5x + 45 ≥ 17 – 9x and 17 – 9x > x + 2

`\implies` 9x – 5x ≥ 17 – 45 and – x – 9x > 2 – 17

`\implies` 4x ≥ – 28 and – 10x > – 15

`\implies` x ≥ – 7 and x < `15/10`

`\implies` x ≥ – 7 and x < `3/2`

Hence solution set `x ∈ [-7, 3/2)` as x ∈ R 

Representation on number line