Question

Assertion (A): If $$8 < 5(x + 1) - 2 \leq 18,\ x\in\mathrm{R}$$, then the smallest integer value of $$x$$ is 0.

Reason (R): Multiplying each side of an inequation by the same integer does not change the inequality.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

Step 1 – Assertion: A is false. $$8 < 5(x + 1) - 2 \le 18$$ $$8 < 5x + 5 - 2 \le 18$$ $$8 < 5x + 3 \le 18$$ $$8 - 3 < 5x \le 18 - 3$$ $$5 < 5x \le 15$$ $$1 < x \le 3$$ Since $$x \in \mathrm{R}$$, the integer values of $$x$$ satisfying the inequation are 2 and 3. Therefore, the smallest integer value of $$x$$ is 2, not 0.

Step 2 – Reason: R is true. Multiplying each side of an inequation by the same positive integer does not change the inequality.