### Video Transcript

Write an inequality to describe the following and then solve it: the quotient of a number and nine is more than two.

We need to take this sentence and write it as a mathematical inequality. To do that, weβll first need to know what quotient means. The quotient is the result of a division problem. If you take a dividend and divide it by a divisor, the result is the quotient. If we have the quotient of a number and nine, weβll let our unknown value be π₯. The quotient of a number and nine will be equal to that number divided by nine, π₯ divided by nine. And that value is more than two.

If itβs more than two, itβs greater than two. So, we use our greater than symbol. And weβre saying that π₯ divided by nine is greater than two, which we could also write as π₯ over nine is greater than two. In addition to writing this inequality, we need to solve for the values of π₯ that make this inequality true. To get π₯ by itself, weβll multiply both sides of the inequality by nine. π₯ over nine times nine equals π₯. And two times nine equals 18.

But what sign do we use? Well, if π is greater than π, and π is greater than zero. If π is positive, then π times π will still be greater than π times π. Because weβve multiplied both sides of this equation by a positive value, the inequality sign doesnβt change. And so, the π₯-values that make this inequality true are π₯-values that are greater than 18. And so, we have π₯ over nine is greater than two and π₯ is greater than 18.