Question

Assertion (A): If 8 < 5(x + 1) – 2 ≤ 18, x ∈ 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

• 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

Both A and R are false

Explanation:

Given,

⇒ 8 < 5(x + 1) – 2 ≤ 18

Solving L.H.S of inequation,

⇒ 8 < 5(x + 1) – 2

⇒ 5(x + 1) – 2 > 8

⇒ 5x + 5 – 2 > 8

⇒ 5x + 3 > 8

⇒ 5x > 8 – 3

⇒ 5x > 5

⇒ `x > 5/5`

⇒ x > 1   ...(1)

Solving R.H.S of inequation,

⇒ 5(x + 1) – 2 ≤ 18

⇒ 5x + 5 – 2 ≤ 18

⇒ 5x + 3 ≤ 18

⇒ 5x ≤ 18 – 3

⇒ 5x ≤ 15

⇒ `x ≤ 15/5`

⇒ x ≤ 3   ...(2)

From (1) and (2), we get :

⇒ 1 < x ≤ 3, x ∈ R

∴ The smallest integer value of x is 2.

∴ Assertion (A) is false.

Multiplying each side of an inequation by the same positive integer does not change inequality, while the inequality changes if multiplied by negative integer.

∴ Reason (R) is false.

Hence, Both A and R are false.