Inequality with fraction and rad

Question

$$2\cdot\sqrt{-5x-1}>5x$$

Tried 5 times but I’m doing something wrong. There’s a step where i should divide in all the possible cases but I don’t understand why and how...

Thanks for the help! :)

Answer 1

Since it must be $\;-5x-1\ge0\iff x\le-\frac15\;$ , the right side is negative, and since the left side is always non-negative, the inequality is true always within its definition domain, i.e.: for any $\;x\le-\frac15\;$