Question

If $\frac{4}{x}\ge 7$, then the range of $x$ is

• A. $(-\infty ,0)$
• B. $(-\infty ,\frac{7}{4}]$
• C. $(0,\frac{4}{7}]$
• D. $(-\infty ,0)\cup [\frac{4}{7},\infty )$

Answer 1

The correct option is C $(0,\frac{4}{7}]$

$\frac{4}{x}\ge 7$
$\Rightarrow \frac{4-7x}{x}\ge 0$
$\Rightarrow \frac{7x-4}{x}\le 0$
Critical points are $\{0,\frac{4}{7}\}$

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$x\in (0,\frac{4}{7}]$