# Question Video: Solving Linear Inequalities by Multiplying by a Negative Number

If 𝑧 + 1 ≤ −9, then −𝑧 ＿.

01:09

### Video Transcript

If 𝑧 plus one is less than or equal to negative nine, then negative 𝑧 blank.

We have the inequality 𝑧 plus one is less than or equal to negative nine. In order for us to find what negative 𝑧 would be equal to, we first need to find 𝑧 by itself. We can do this by subtracting one from either side of this inequality. And we see that 𝑧 is less than or equal to negative 10. If we want to know something about negative 𝑧, we could multiply the entire inequality by negative one. But we have to remember that when we’re multiplying inequalities by negative values, we need to flip the sign. And that means we’ll have to change it from a less than or equal to to a greater than or equal to.

After that, we multiply through by negative one just like we would in an equation so that we have negative 𝑧. And then, negative one times negative 10 is positive 10. If 𝑧 is less than or equal to negative 10, then negative 𝑧 will be greater than or equal to positive 10 .