Question

If x∈R, solve `2x - 3 ≥ x + (1 - x)/(3) > (2)/(5)x`

Answer 1

`2x - 3 ≥ x + (1 - x)/(3) > (2)/(5)x`

`2x - 3 ≥ x + (1 - x)/(3) and x + (1 - x)/(3) > (2)/(5)x`

`2x - 3 ≥ (3x + 1 - x)/(3) and (3x + 1 - x)/(3) > (2)/(5)x`

6x - 9 ≥ 3x + 1 - x and 15x + 5 - 5x > 6x

6x - 3x + x ≥ 1 + 9 and 15x - 6x - 5x > -5

4x ≥ 10 and 4x > -5

`x ≥ (10)/(4) and x > -(5)/(4)`

`x ≥ (5)/(2)and x > -(5)/(4)`

From left side we get `x ≥ (5)/(2)` and from right side we get `x > -(5)/(4)`

`x ≥ (5)/(2`

∴ Solution set = `{x : x ∈ "R", x ≥ (5)/(2)}`

The graph of the inequation is represented by thick black line starting from `5/2` (including `5/2`).