How to Divide Inequalities

Video Transcript

"Let's take a look at dividing inequalities. Let's say, you have 2x or let's say 3-2x is greater than 5. And let's take a look at 2 actually at the same time. This one and also 2 3x is less than 4. So here's the deal with dividing inequality. Or solving an inequality, let's say. The most important thing is, when you solve an inequality. You're going to do what exactly like you would a normal equation. So we're going to subtract, let's do this one first. We're going to subtract 2 from both sides. 2 minus 2 cancels, there's going to be 3x. Is less than, you just copy the sign. 4-2 is 2. Now you divide, this is where this comes in. You divide both sides by 3. 3 over 3 cancels, that's why we did it. x is less than two thirds, there's your answer. We solved it exactly like we would if there were an equal sign there. Except, it happens to be a less than sign. But when we have this one, you're going to see something else happen. So subtract 3 by both sides. 3 minus 3 cancels. That's why we did it. Negative 2x, greater than 5 minus 3 is 2. Now we're going to divide both sides by negative 2, to get the x alone. This is the one trick, when you divide an inequality sign. Means not an equal sign. When you divide an inequality by a negative number, we flip the inequality sign. We change it, we reverse it. So this cancels, that's why we did it. Gives me X alone. 2 over negative 2 is negative 1. And instead of being greater than, it's going to be less than. So the one trick to dividing inequalities, is when you divide or multiply by a negative number. You swap, you flip the inequality sign."