Question

Solve the inequation given below. Write the solution set and represent it on the number line:

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

Answer 1

Given,

`4x - 19 < (3x)/5 - 2 ≤ (-2)/5 + x`

Solving L.H.S. of the equation,

⇒ `4x - 19 < (3x)/5 - 2`

⇒ `4x - 19 < (3x - 10)/5`

⇒ 5(4x – 19) < 3x – 10

⇒ 20x – 95 < 3x – 10

⇒ 20x – 3x < 95 – 10

⇒ 17x < 85

⇒ x < 5   ...(i)

Solving R.H.S. of the equation,

⇒ `(3x)/5 - 2 ≤ - 2/5 + x`

⇒ `x - (3x)/5 ≥ -2 + 2/5`

⇒ `(5x - 3x)/5 ≥ (-10 + 2)/5`

⇒ `(2x)/5 ≥ (-8)/5`

⇒ `x ≥ - 8/5 xx 5/2`

⇒ x ≥ –4   ...(ii)

From (i) and (ii) we get,

–4 ≤ x < 5

∴ Solution set = {x : –4 ≤ x < 5, x ∈ R}.

Solution on the number line is: