Inequality Implication Reasoning – UGC NET Question

The condition x > 3 tells us that x is strictly greater than 3 on the number line. Adding the same number to both sides of an inequality preserves its direction, so adding 2 to get x + 2 > 3 + 2 shows that x + 2 > 5. This relationship must hold for every x satisfying the original inequality.

Option A:
Option A follows directly from adding 2 to both sides of the original inequality. Since 3 + 2 equals 5, every value of x greater than 3 will make x + 2 greater than 5 as well.

Option B:
Option B, x − 5 > 0, would require x to be greater than 5, which is stronger than the given condition. Since x may be between 3 and 5, this statement need not always be true.

Option C:
Option C, 2x < 6, implies x < 3, which actually contradicts the assumption that x is greater than 3. Option D: Option D, x/2 < 1.5, is another form of x < 3 and thus conflicts with the original inequality rather than following from it.