Which of the following inequalities, where $x$ is an integer, is/are satisfied by the solution set $x = 3, 4, 5 ?$
$(I)$ $3 x > 9$ $(I I)$ $x - 1 \geq 2$ $(I I I)$ $x + 3 \geq 5$

I I

only

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I

and

I I

only

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I I

and

I I I

only

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I, I I

and

I I I

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Solution

The correct option is C $I I$ and $I I I$ only
Consider the given three inequalities for the solution set $x = 3, 4, 5$
Therefore, substituting $3$ in all the three inequalities
1) $3 x > 9$
$9 > 9$ false ( $9 = 9$ and is not greater the $9$ )
Therefore, given values of $x$ are not the solution of above inequality.
2) $x - 1 \geq 2$
$\Rightarrow x \geq 2 + 1 \Rightarrow x \geq 3$ and $x$ is an integer
Hence, given values of $x$ are the solution of above inequality.
3) $x + 3 \geq 5$
Therefore, $x > 5 - 3$ or $x > 2$ and $x$ is an integer
Hence, given values of $x$ are the solution of above inequality.
Hence, the answer is option $C$ .

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Which of the following inequalities, where x is an integer, is/are satisfied by the solution set x=3,4,5?(I) 3x>9 (II) x−1≥2 (III) x+3≥5

Which of the following inequalities, where $x$ is an integer, is/are satisfied by the solution set $x = 3, 4, 5 ?$
$(I)$ $3 x > 9$ $(I I)$ $x - 1 \geq 2$ $(I I I)$ $x + 3 \geq 5$