# Video: Writing and Solving Linear Inequalities

Given that seven times a number is less than 21, write an inequality to describe this information, and then solve it.

02:10

### Video Transcript

Given that seven times a number is less than 21, write an inequality to describe this information and then solve it.

So in this question, the first thing we need to do is actually have a look at the information we’ve got. And we’re told that seven times a number is less than 21. So this is what we need to write an inequality to describe. So what I’m gonna do is I’m gonna call our number 𝑥. So that’s just 𝑥. And then, I’m gonna write seven 𝑥 and that’s because seven times a number is actually seven multiplied by 𝑥. And that’s how we write it.

We then have this sign, which looks like this. And this sign means less than. And we know it means less than cause the thinner, so the pointy end is actually pointing towards our seven 𝑥. And I’ve actually shown this on a little sketch on the right-hand side. So here, we can say 𝑥 is greater than when actually the 𝑥 is where the open mouth of our inequality sign is, but 𝑥 is less than when it’s actually the point all it comes together. That means that’s when 𝑥 is less than something.

And we also know that actually it doesn’t have a line underneath because if you have a line underneath in an inequality sign this means or equal to. Okay, great, so seven 𝑥 is less than, so seven times a number is less than, 21 because that’s what it tells us in the question. So great! We’ve actually solved the first part of the question because it says write an inequality to describe the information. So we’ve got seven 𝑥 is less than 21.

And now, we’re actually gonna move on to the second part because the second part of the question says solve it. So when we’re gonna solve an inequality like this, so a linear inequality, we just solve it in the same way we’d solve an equation. So therefore, if we have seven 𝑥 is less than 21 and we want to know what 𝑥 is, then we’ll actually divide each side of the inequality by seven.

And when we do that, we get 𝑥 is less than three. And that’s because seven 𝑥 divided by seven is just 𝑥 and 21 divided by seven is three. So therefore, we’ve solved the second part as well.

So what we can say is that given that seven times a number is less than 21, the inequality that describes this is seven 𝑥 is less than 21. And then, the solution to it is 𝑥 is less than three.