Question

1/x<4x

`(1)/(x) < 4x`
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Answer 1

`x>(1)/(2) \\x<(-1)/(2)`

Explanation:

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

we have
`(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{(1)/(4) } < \sqrt{x^(2) }`

This leaves to the following

`(1)/(4)<|x|`

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

so

`x>(1)/(2) \\x<(-1)/(2)`