Question

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. 3x + 1 ≤ 17, then greatest natural number satisfying this inequation is 5.
2. 1 − 3x ≤ 2x − 3, then least integer value of x is 1.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

Statement (i)

3x + 1 ≤ 17

3x ≤ 16

⇒ x ≤ `16/3`

≈ 5.33

Natural numbers satisfying this are:

{1, 2, 3, 4, 5}

The greatest natural number is 5.

Statement (ii)

1 − 3x ≤ 2x − 3

1 + 3 ≤ 2x + 3x

⇒ 4 ≤ 5x

⇒ x ≥ `4/5`

{1, 2, 3, …}

The least integer value is 1.