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If x satisf...

Question

If $x$ satisfies the inequalities $x + 7 < 2 x + 3$ and $2 x + 4 < 5 x + 3$ , then $x$ lies in the interval.

(- \infty, 3)

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(1, 3)

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(4, \infty)

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(- \infty, - 1)

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(3, 4)

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Solution

The correct option is D $(4, \infty)$
Given,
$x + 7 < 2 x + 3$
$\Rightarrow 4 < x \Rightarrow x > 4$ .... (i)
and $2 x + 4 < 5 x + 3$

$\Rightarrow 1 < 3 x \Rightarrow x > \frac{1}{3}$ .... (ii)
From Eqs. (i) and (ii), we get the common interval $(4, \infty)$ i.e., $x \in (4, \infty)$ .

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