Why is x < -¼?

[hybrid sleet]

-4 < 1/x

-4x < 1

divide both sides by a negative number (which is -4), this should flip the inequality sign but it doesn't

x > -¼ ( this is wrong)

it should he x < -¼

but how and why?

[mortal wyvern]

the first step is wrong

you can't multiply by x on both sides if you don't know its sign

it would flip the inequality sign if x were negative

[hybrid sleet]

oh

yeah there's a possibility it could be a negative

but how would i know that x is less than -¼?

[mortal wyvern]

i think you have to consider both cases

if x is positive then 1/x < 3 implies x > 1/3

if x is negative then same thing with -1/4

[mortal wyvern]

(most of the time when the domain is not an interval you need to split it into multiple ones and then everything works on those)

[gloomy salmon]

don't forget to close if it is already resolved

[hybrid sleet]

.solved