Question

Solve : `(4x - 10)/(3) ≤ (5x - 7)/(2)` x ∈ R and represent the solution set on the number line.

Answer 1

`(4x - 10)/(3) ≤ (5x - 7)/(2)`
⇒ 8x – 20 ≤ 15x – 21    ...(L.C.M. of 3, 2 = 6)
⇒ 8x - 15x ≤ - 21 + 20
⇒ -7x ≤ - 1

⇒ -x ≤ - `(1)/(7)`

⇒ x > `(1)/(7)`
∵ x ∈ R
∴ Solution set = {x : x ∈ R, x > `(1)/(7)`}
Solution set on the number line