Question

Solve for x : $\frac{3}{x}$ < 5

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\frac{3}{x}$ < 5 $\Rightarrow$ $\frac{3}{x}$ - 5 < 0

(we cannot cross multiply with 'x' as 'x' can be negative or positive)

$\Rightarrow$ $\frac{3-5x}{x}$ < 0

$\Rightarrow$ $\frac{5x-3}{x}$ > 0

$\Rightarrow$ $\frac{(x-\frac{3}{5})}{(x-0)}$ > 0

Sign scheme of above expression is shown below

$\Rightarrow$ x ∈ ($-\infty$,0) U ($\frac{3}{5}$,$\infty$)