Question

If x ∈ Z, solve 2 + 4x < 2x – 5 ≤ 3x. Also represent its solution on the number line.

Answer 1

2 + 4x < 2x – 5 ≤ 3x
2 + 4x < 2x – 5 and 2x – 5 ≤ 3x => 4x – 2x < – 5 – 2 ,and 2x – 3x ≤ 5
⇒ 2x < - 7 and - x ≤ 5

⇒ `x < -(7)/(2)` and x ≥ - 5 and - 5 ≤ x

∴ - 5 ≤ x < - `(7)/(2)`
∵ x ∈ Z
∴ Solution set = {-5, -4}
Solution set on Number line