Question

Assertion (A): For the inequation –12 < 3 – 4x ≤ 11, x ∈ N, the solution set is {1, 2, 3, 4}.

Reason (R): The set of all those values of x from the replacement set which satisfy the given inequation is called the solution set of the inequation.

पर्याय

• A is true, R is false

• A is false, R is true

• Both A and R are true

• Both A and R are false

Answer 1

A is false, R is true

Explanation:

Given,

⇒ –12 < 3 – 4x ≤ 11

Solving L.H.S of inequation,

⇒ –12 < 3 – 4x

⇒ 4x < 3 + 12

⇒ 4x < 15

⇒ `x < 15/4`

⇒ x < 3.75   ...(1)

Solving R.H.S of inequation,

⇒ 3 – 4x ≤ 11

⇒ 11 ≥ 3 – 4x

⇒ 4x ≥ 3 – 11

⇒ 4x ≥ –8

Dividing by 4 on both sides we get,

⇒ x ≥ –2   ...(2)

From (1) and (2) we get,

⇒ –2 ≤ x < 3.75

Since x ∈ N

Solution set = {1, 2, 3}

∴ Assertion (A) is false.

We know that,

The set of all those values of x from the replacement set which satisfy the given in equation is called the solution set of inequation.

∴ Reason (R) is true.