Which of the following graphs represent the solution of the inequation written below:

$2 x - 5 \leq 5 x + 4 < 11, x ϵ R$

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None of these

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Solution

The correct option is A

$2 x - 5 \leq 5 x + 4 < 11$
$\Rightarrow 2 x - 5 \leq 5 x + 4 a n d 5 x + 4 < 11$
$\Rightarrow - 5 - 4 \leq 5 x - 2 x a n d 5 x < 11 - 4$
$\Rightarrow - 9 \leq 3 x a n d 5 x < 7$
$\Rightarrow - 3 \leq x a n d x < \frac{7}{5}$
$\Rightarrow - 3 \leq x < \frac{7}{5}$
$\Rightarrow - 3 \leq x < \frac{7}{5}$

$B u t, x ϵ R {x : - 3 \leq x < (\frac{7}{5}), x ϵ R}$

The graph of the solution set is shown in the following figure

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