Given that x is an integer, find the values of x which satisfy both $2 x + 3 > 7$ and $x + 4 < 10$ .

3

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4

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4

and

5

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3, 4

and

5

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Solution

The correct option is D $3, 4$ and $5$
$2 x + 3 > 7$
Add $- 3$ on both sides, we get
$2 x + 3 - 3 > 7 - 3$
$\Rightarrow 2 x > 4$
Dividing by $2$ , we get
$x > 2$ (3,4,5..........)
Also,
$x + 4 < 10$
Add $- 4$ on both sides, we get
$x + 4 - 4 < 10 - 4$
$\Rightarrow x < 6$ (........2,3,4,5)
Then, $x = 3, 4$ and $5$ .

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