# How do you write the inequality and solve "the product of -5 and a number is greater than 35 or less than 10#?

Dec 28, 2017

$x < - 7$ or $x > - 2$

#### Explanation:

Let $x$ be "the number."

The product of $- 5$ and a number can be represented as $- 5 x$.

We know that $- 5 x > 35 \setminus \rightarrow x < - 7$. (Don't forget to change the sign when you divide by a negative!)

We also know that $- 5 x < 10 \setminus \rightarrow x > - 2$. (We flipped the sign again.)

So the solution is $x < - 7$ or $x > - 2$.