Assertion: If (a<b), then (a+c<b+c). Reason: Adding the same number to both sides does not change the direction of an inequality. Choose the correct option.

Correct answer: both assertion and reason are true, and the reason explains it

The direct answer is A: both the assertion and reason are true, and the reason correctly explains the assertion. Start with a<b. Adding the same number c to both sides gives a+c<b+c. This operation shifts both numbers equally on the number line, so their order does not change. No restriction is needed on c; it may be positive, zero, or negative. A is correct because the reason states exactly the rule used in the proof. B is wrong because the reason is not merely true separately—it directly justifies the assertion. C is wrong because the reason is true, not false. D is wrong because the assertion is true, not false. Do not confuse addition with multiplying or dividing by a negative number: adding the same quantity preserves the inequality direction. Exam cue: add or subtract the same number on both sides, and the sign stays unchanged.