Question

Solve the following inequation, write the solution set and represent it on the number line.

`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`

Answer 1

`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`

`\implies -3 (x - 7) ≥ 15 - 7x` and `15 - 7x > (x + 1)/3`

`\implies` –3x + 21 ≥ 15 – 7x and 45 – 21 > x + 1

`\implies` 4x ≥ –6 and 44 > 22x

`\implies x ≥ (-3)/2` and `2 > x`

`\implies` x ≥ –1.5 and 2 > x

The solution set is {x : x ∈ R, –1.5 ≤ x < 2}

The solution set is represented on number line as follows: