Which one of the following inequalities are satisfied by x=10 ?

The correct answer is Option (3) → \( \displaystyle\frac{2x-5}{4}\lt10,\ x\in\mathrm{R} \)

Substituting x = 10 in each inequality:

Option (1) \( \displaystyle\frac{2x-5}{4}\gt10,\ x\in\mathrm{R} \) — Incorrect. \( \frac{20-5}{4}=3.75 \), which is not greater than 10.

Option (2) \( \displaystyle\frac{5x-2}{4}\lt10,\ x\in\mathrm{R} \) — Incorrect. \( \frac{50-2}{4}=12 \), which is not less than 10.

Option (3) \( \displaystyle\frac{2x-5}{4}\lt10,\ x\in\mathrm{R} \) — Correct. \( \frac{20-5}{4}=3.75 \), which is less than 10.

Option (4) \( \displaystyle\frac{2-5x}{4}\gt10,\ x\in\mathrm{R} \) — Incorrect. \( \frac{2-50}{4}=-12 \), which is not greater than 10.