Question

If $\frac{5}{x}+\frac{3}{2x}\le 26,x>0$, then

• A. $x\ge \frac{1}{4}$
• B. $0<x\le \frac{1}{4}$
• C. $0<x<\frac{1}{4}$

Answer 1

The correct option is A $x\ge \frac{1}{4}$

We know that x > 0,
$\Rightarrow$ We can multiply both sides of the inequality by 2x without flipping the inequality sign.
Multiplying both sides by $2x$
$\Rightarrow 10+3\le 52x$
Now, dividing both sides by $52$
$\Rightarrow 52x\ge 13$
$\Rightarrow x\ge \frac{1}{4}$