Inequalities — Assertion-Reason Type Questions

Assertion (A): Given, $15x - 10 \lt 4x + 2$

$\Rightarrow 15x - 4x \gt 10 + 2$

Reason (R): We can add the same number or expression to both sides of an inequation.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Given,,

$\Rightarrow 15x - 10 \lt 4x + 2$

Transposing $4x$ to L.H.S. and -10 to R.H.S.,

$\Rightarrow 15x - 4x \lt 2 + 10$

∴ Assertion (A) is true.

Adding the same number or expression to both the sides of an inequation does not change the inequality.

∴ Reason (R) is true.

Hence, Option 3 is the correct answer.

Assertion (A): $3x + 5 \lt 65$ is not an inequation.

Reason (R): If the replacement set is not defined, then solution of the inequality can't be represented on a number line.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

$3x + 5 \lt 65$ is a mathematical statement showing that the two expressions are not equal and it involves the variable $x$.

∴ $3x + 5 \lt 65$ is an in-equation.

∴ Assertion (A) is false.

The solution set of an inequation is chosen from the replacement set. So, if the replacement set is not defined, the solution of the inequality cannot be represented on a number line.

∴ Reason (R) is true.

Hence, Option 2 is the correct answer.

Assertion (A): $3 \gt -x \ge -5 \Rightarrow -3 \lt x \le 5$

Reason (R): If the same quantity is subtracted from both the sides of an inequation, the sign of inequality does not change.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Given, $3 \gt -x \ge -5$

Multiplying each side by -1, the inequality gets reversed.

$\Rightarrow -3 \lt x \le 5$

∴ Assertion (A) is true.

Subtracting the same quantity from both the sides of an inequation does not change the sign of inequality.

∴ Reason (R) is true.

Hence, Option 3 is the correct answer.