Question

1/x<4x
$\frac{1}{x} < 4x$
​

Answer 1

Answer:

$x>\frac{1}{2} \\x<\frac{-1}{2}$

Step-by-step explanation:

If we solve for 'x' variable, its recommended to multiply 'x' variable in both sides of inequality:

we have $\frac{1}{4}< x^{2}$

This is a quadratic equation, two answer are going to be obtained from here.

since $\sqrt{x^{2} } = |x|$

Applying square roots to both sides of inequality sign we wil have the following

$\sqrt{\frac{1}{4} } < \sqrt{x^{2} }$

This leaves to the following

$\frac{1}{4}<|x|$

remember that $|x|= +/ - x$

so

$x>\frac{1}{2} \\x<\frac{-1}{2}$