Question

Solve the following inequation and represent the solution set on the number line:
`4x - 19 < (3x)/(5) -2 ≤ (-2)/(5)+ x , x ∈ "R"`

Answer 1

`4x - 19 < (3x)/(5) -2 ≤ (-2)/(5)+ x , x ∈ "R"`

∴ `4x  - 19 < (3x)/(5) - 2`,

`4x - (3x)/(5) <- 2 + 19`

`(17x)/(5) < 17`,
x < 5,
and  `(3x)/(5) - 2 ≤ (-2)/(5) + x`

`(3x)/(5) - x ≤ (-2)/(5) + 2`
-2x ≤ 8
x ≥ - 4
⇒ - 4 ≤ x ≤ 5