Question

Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N

Answer 1

1 ≥ 15 – 7x > 2x – 27
1 ≥ 15 – 7x and 15 – 7x > 2x – 27
⇒ 7x ≥ 15 - 1 and - 7x - 2x > - 27 - 15
⇒ 7x ≥ 14 and -9x > - 42

⇒ x ≥ 2 and -x > `-(42)/(9)`

⇒ 2 ≤ x and -x > `-(14)/(3) and x < (14)/(3)`

2 ≤ x < `(14)/(3)`
But x ∈ N
∴ Solution set = {2, 3, 4}.