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

$2 x - 5 \leq 5 x + 4 < 11 \Rightarrow 2 x - 5 \leq 5 x + 4$ and $5 x + 4 < 11 \Rightarrow - 5 - 4 \leq 5 x - 2 x$ and $5 x < 11 - 4 \Rightarrow - 9 \leq 3 x$ and $5 x < 7 \Rightarrow - 3 \leq x$ and $x < (\frac{7}{5}) \Rightarrow - 3 \leq x < (\frac{7}{5}) \Rightarrow - 3 \leq x < (\frac{7}{5})$

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

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

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Similar questions

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

$2 x - 5 \leq 5 x + 4 < 11, x ϵ R$

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

$2 x - 5 \leq 5 x + 4 < 11, x ϵ R$

Which of the following number line represents the solution of the inequation:
$2 + 4 x < 2 x - 5 \leq 3 x; x \in Z$ .

2 x - 5 \leq 5 x + 4 < 11, w h e r e x ϵ I

- 3 < - \frac{1}{2} - \frac{2 x}{3} \leq \frac{5}{6}, x ϵ R

$If x ϵ Z, solve the inequation 2 + 4 x < 2 x - 5 \leq 3 x . Also, represent its solution set on a number line.$

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