Question

What are the solutions to the inequality (x-3)(x+5) <0?

o {X33X55)
o {X/-55X5-3)
o {x\-55x53)
{x-35x35)

Answer 1

You want a product to be negative. A product is negative if and only if the two factors have opposite signs.

So, there are two cases: either
`x-3` is positive and
`x+5` is negative, or vice versa. But since
`x-3` is less than
`x+5`, the only possibility is that

`\begin{cases}x-3<0\\x+5>0\end{cases} \iff \begin{cases}x<3\\x>-5\end{cases}`

So, the solution is given by all numbers
`x` such that

`-5<x<3`