Question

`-3/2 ≥ -(2x)/3` where x ∈ R.

Assertion (A): The largest value of x is `9/4`.

Reason (R): When the signs of both the sides of an inequation are changed, the sign of inequality reverses.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

According to the assertion:

⇒ `−3/2 ≤ −(2x)/3`

⇒ `3/2 ≥ (2x)/3`

⇒ `x ≤ (3×3)/(2×2)`

⇒ x ≤ 94

So, Assertion (A) is true.

According to the reason:

When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign must be reversed to keep the inequality valid.

So, Reason (R) is true.