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"`
Hence, solution set is {x : -4 < x < 5, x ∈ R}
The solution set is represented on the number line as below.

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

⇒ `4x - (3x)/(5) < 17 and 2 + (2)/(5) ≤ x - (3x)/(5), x ∈ "R"`

⇒ `(17x)/(5) < 17 and (-8)/(5) < (2x)/(5), x ∈ "R"`
⇒ x < 5 and –4 ≤ x,  x ∈ R
⇒ –4 ≤ x < 5, x ∈ R
Hence, solution set is {x : –4 ≤  x < 5, x ∈ R}
The solution set is represented on the number line as below.