Question Video: Writing and Solving One-Step Linear Inequality Word Problems Mathematics • 6th Grade

Write an inequality to describe the following, and then solve it: The quotient of a number and 9 is more than 2.

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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, we’ll 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, we’ll 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 it’s more than two, it’s greater than two. So, we use our greater than symbol. And we’re 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, we’ll 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‘Ž is greater than 𝑏, and 𝑐 is greater than zero. If 𝑐 is positive, then π‘Ž times 𝑐 will still be greater than 𝑏 times 𝑐. Because we’ve multiplied both sides of this equation by a positive value, the inequality sign doesn’t 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.

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