How to Do Inequalities

How to do inequalities? I'm Bon Crowder with MathFour.com and we're looking at how to do inequalities. Now, there's a whole variety of different inequalities that we could do. I picked one that's a little bit more complex, that goes in a range. So, here we have negative five, is greater than or equal to, I'm sorry is less than or equal to negative two-X plus one. It goes to three and that's less than three. So, I'm going to start out with that. So, negative two-X plus one is in this range. And then, I'm going to start moving along the number line. So, the next thing I'm going to do is subtract one. But I have to subtract it from both sides, but there's really two inequalities here. So, I'm going to subtract it like that. So, negative five minus one is negative six. Less than or equal to negative two-X, these make zero, so cancel, is less than two. So, what we've done is, moved this whole thing to here. So, we've actually shifted to left, one unit. Next, we get to divide by negative two. Again, doing it on all three parts because it's really both sides. Now, here's where the kicker comes in. Any time you multiply or divide by a negative number, it turns the entire number line around. Which means you have to switch these inequalities. So, this is less than, so I'm going to change it to greater than or equal to. And this one, likewise, I'm going to do that. So, this is negative six divided by negative two, is positive three. The negative two's make a one, so they cancel. And then, i have two divided by negative two, is negative one. Which means I'm going from negative one, is less than X, is less than or equal to three. So, I go from negative one to three, inclusive. So, the way it moves on the number line, is the same way it moves when you're doing the problem. The only thing to really remember is, that when you multiply and divide by that negative. You've got to flip both inequalities symbols over. I'm Bon Crowder with MathFour.com and that's how you do an inequality.