Question

Assertion (A): If $$2x - 5 \leq 5x + 4 < 11, \ x \in \mathrm{I}$$, then the greatest value of $$x$$ is 1.

Reason (R): Adding or subtracting a negative integer to each side of an inequation reverses 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 true, but R is false.

Explanation:

Step 1 – Assertion: A is true. The compound inequation gives $$-3 \leq  x < \frac{7}{5}$$. For $$x \in \mathrm{I}$$, the solution set is {–3, –2, –1, 0, 1}, whose greatest value is 1.

Step 2 – Reason: R is false. Adding or subtracting the same number from both sides does not change the inequality. It is multiplying or dividing both sides by a negative number that reverses the inequality.