Video: Creating Linear Inequalities with One Variable

Mr Benjamin tells his class, “Two more than ten times a number is at least 50.” Let 𝑥 represent the number, and write an inequality to represent his statement.

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Video Transcript

Mr Benjamin tells his class, “Two more than 10 times a number is at least 50.” Let 𝑥 represent the number, and write an inequality to represent his statement.

Well, to solve this problem, we’re gonna deal with it in steps. So we’re gonna work backwards. So we’ve got our number, which is 𝑥. Well first of all, we want to write 10 times a number. Or to write 10 times 𝑥, we just write a 10 in front of the 𝑥. So we’ve got 10𝑥. So as we’ve said, that’s that part dealt with, so 10 times a number.

So now what we want to look at is two more than this. So for two more than, we just write add two. So now we’ve got two more than 10 times a number. So we’ve got 10𝑥, which is 10 times a number, then plus two, so two more than this.

And then, we look at the next part. And we’re told that 10𝑥 plus two, so two more than 10 times a number, is at least 50. And the key bit here is “at least” because this tells us what inequality sign we’re gonna have, because “at least 50” means that it can be greater than or equal to 50 because we’re told that the very least here is 50, which means it can be 50.

So that’s why I’ve drawn this shape here or this inequality sign here. And this bottom line means or equal to. What this also means is that 10𝑥 plus two is greater than. And that’s because the wide end or the open end is by this. And then, all we’ve to write in is 50 because we know that it’s at least 50.

So we can say that if Mr Benjamin tells his class “two more than 10 times a number is at least 50” and letting 𝑥 represent the number, the inequality to represent his statement is 10𝑥 plus two is greater than or equal to 50.

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