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Solve $-5(x-1) \leq 10(2 x-3)$

Option: 1
$\left(-\infty, \frac{7}{5}\right)$

Option: 2
$\left(-\infty, \frac{7}{5}\right]$

Option: 3
$\left(\frac{7}{5}, \infty\right)$

Option: 4
$\left[\frac{7}{5}, \infty\right)$

Answers (1)

best_answer

The correct option is (d)

$\begin{aligned} -5(x-1) & \leqslant 010(2 x-3) \\ \Rightarrow \quad(x-1) & \geqslant \frac{10}{-5}(2 x-3) \end{aligned}$

$\begin{aligned} &\Rightarrow x-1 \geqslant-2(2 x-3) \\ &\Rightarrow x-1 \geqslant-4 x+6 \\ &\Rightarrow x+4 x \geqslant 6+1 \\ &\Rightarrow 5 x \geqslant 7 \\ &\Rightarrow x \geqslant \frac{7}{5} \end{aligned}$

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Ajit Kumar Dubey

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