Question

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

`2x - 1 ≥ x + (7 - x)/3 > 2, x ∈ R`

Answer 1

Given,

⇒ `2x - 1 ≥ x + (7 - x)/3 > 2, x ∈ R`

Solving L.H.S. of the inequation,

⇒ `2x - 1 ≥ x + ((7 - x))/3`

⇒ `2x - x > ((7 - x))/3 + 1`

⇒ `x ≥ (7 - x + 3)/3`

⇒ `x ≥ (10 - x)/3`

⇒ 3x ≥ 10 – x

⇒ 3x + x ≥ 10

⇒ 4x ≥ 10 

⇒ `x ≥ 10/4`

⇒ `x ≥ 5/2`   ...(1)

Solving R.H.S. of the inequation,

⇒ `x + ((7 - x))/3 > 2`

⇒ `(3x + 7 - x)/3 > 2`

⇒ `(2x + 7)/3 > 2`

⇒ 2x + 7 > 6

⇒ 2x > 6 – 7

⇒ 2x < –1

⇒ `x > –1/2`

⇒ x > –0.5   ...(2

From (1) and (2) we get,

`x ≥ 5/2`

Hence, solution set = `{x : x ≥ 5/2, x ∈ R}`.

Solution on the number line is: