Question

Find the unknown in $\frac{1}{x}\le \frac{2}{3}$, if $x$ is a positive number.

• A. $\frac{2}{3}\le x$
• B. $\frac{3}{2}\le x$
• C. $\frac{2}{3}\ge x$
• D. $\frac{3}{2}\ge x$

Answer 1

The correct option is B $\frac{3}{2}\le x$

Given, $\frac{1}{x}\le \frac{2}{3}$

Multiply both side by $x$, as multiplying by $x$ will not change the inequality sign because $x$ is a positive number.
$\frac{1}{x}\times x\le \frac{2}{3}\times x$
$1\le \frac{2x}{3}$

Multiply both side by 3
$1\times 3\le \frac{2x}{3}\times 3$
$3\le 2x$

Transfer 2 to L.H.S
$\frac{3}{2}\le x$
Hence, option (b.) is the correct choice.