Question

Solve the inequation given below and represent its solution set on a number line:

`(5x - 8)/3 ≥ (4x - 7)/2, x ∈ R`

Answer 1

Given,

⇒ `(5x - 8)/3 ≥ (4x - 7)/2`

Multiplying by 6 on both sides we get,

⇒ `6((5x - 8)/3) ≥ 6((4x - 7)/2)`

⇒ 2(5x – 8) ≥ 3(4x – 7)

⇒ 10x – 16 ≥ 12x – 21

⇒ 10x – 12x ≥ –21 + 16

⇒ –2x ≥ –5

Dividing by –2 on both sides we get,

⇒ `x ≤ 5/2`   ...(As on dividing by negative number the sign reverses)

Since, x ∈ R

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

Solution on the number line is: