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Solve Inequalities Using Multiplication and Division - Example 4

In mathematics, an inequality is a conditional statement that is either true or false, depending on the value of the variable.


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Video Transcript

So in this example we're freeing. Asked to write it inequality to represent the given freeze. Then we're going to solve the inequality and graft. The solution set on number one, while our phrase Rees, the product of negative two and a number, is at most 18. So let's break this down. While the first thing it says is the product will remember, product means multiplication. Well, what are we multiplying? We're multiplying negative to buy a number. And remember, when we don't know what the number is, we're gonna call it X. So how would we represent the product of negative two and a number that would be just negative? Two X Okay for our next phrase, it says is at most well, let's think about what this means. If you have, at most $10 that means you could have $10 but that's the highest amount you could have. You could have anything less than it, but that is the most you could have. So is that most means less than or equal to. So that's gonna be our inequality sign. Less than or equal to, Well, what is it less than equal to? It says it's at most 18. So now we've written our inequality. It's negative. Two X is less than or equal to 18. Okay, now that we have are in their quality, we want to go ahead and solve. So we saw just like normal. So to get X by itself, we're going to divide both sides of our inequality by negative too. But remember, we're dividing both sides by a negative value, which means we have to flip our inequality sign. Therefore, the less than or equal to will become greater than or equal to. And then we divide like normal 18 divided by negative two is negative night. So now we have solved our inequality. The last thing we're asked to dio is graft. A solution set on the number line so we can set up our number line. We can put our critical number negative nine right in the middle. Next will determine if we need the open or close circle. Well, negative nine would be a solution in this case because of the or equal to. So this is going to be a close circle and now we'll figure out to shade to the left or to the right Well, because our values of X have to be greater than a regular negative nine. Our values of X that would be greater than would occur to the right of negative nine on our number line. So now we've written our inequality. We've solved it and we've drafted solution set on a number line.