A rectangle has a length of eight inches and an area less than 40 square inches. Write and solve an inequality to determine its width.
Well first, I’m gonna do with this problem is just draw all the rectangle. It’s just gonna help us to see what we have, what information we’ve got. Well, we can see the information we have, that the length is equal to eight. The width is what we try to find out, so we don’t know our width, and the area is less than 40. And remembering that we use the sign for less than 40 without the line below because if we have the line below, that means “or equal to”. And in the question, it just says the area is less than 40 square inches.
Okay, so in order to start solving the problem, we can say that the area is equal to the length multiplied by the width. And therefore, we can say that 𝐴, so our area is equal to eight 𝑤 because we substituted in that our length is equal to eight. And therefore, we can say that eight 𝑤, because that’s what our area is, has to be less than 40. So there we have it; we formed the inequality.
So that’s the first part of our problem, solved. Great, now what we need to do is to actually solve that inequality to determine the width. But when we solve the inequality, we solve it in the same way that we’d solve an equation. So we can divide both sides by eight. So therefore, we get 40 divided by eight which gives us five. So we can say that 𝑤 is less than five. So we’ve now completed both parts of the question.