In the following question, two statements (i) and (ii) are given. Choose the valid statement. i. 3x + 1 $\leq$ 17, then greatest natural number satisfying this inequation is 5. ii. 1 − 3x $\leq$ 2x − 3, then least integer value of x is 1.

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Both (i) and (ii) Explanation: Statement (i) 3x + 1 $\leq$ 17 3x $\leq$ 16 $\Rightarrow$ x $\leq$ $\frac{16}{3}$ ≈ 5.33 Natural numbers satisfying this are: {1, 2, 3, 4, 5} The greatest natural number is 5. Statement (ii) 1 − 3x $\leq$ 2x − 3 1 + 3 $\leq$ 2x + 3x $\Rightarrow$ 4 $\leq$ 5x $\Rightarrow$ x $\geq$ $\frac{4}{5}$ {1, 2, 3, …} The least integer value is 1.

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