Question Video: Writing Double Inequalities Mathematics • 6th Grade

Rewrite the statement “𝑦 is between 8 and 10” using <, ⩽, >, or ⩾.

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Video Transcript

Rewrite the statement 𝑦 is between eight and 10 using our inequality notation.

So what we’ve done here is drawn a little sketch just to help us understand what’s going on. So we know that 𝑦 is between eight and 10. However, as we can see in the statement, we’re told that 𝑦 is between eight and 10. So therefore, it cannot be eight or 10. So therefore, we’ve got to say that 𝑦 is gonna be greater than eight, but it’s gotta be less than 10. And that’s because if we just said that 𝑦 was greater than eight, then it can be anything that was greater than eight at all. But we’re told that it’s between eight and 10. But as we said, it doesn’t include eight or 10. So that’s why we use our compound inequality notation or double inequality notation we’ve used here.

And we’ve shown the 𝑦 between our eight and 10. And then we’ve used our inequality signs showing that 𝑦 is in fact greater than eight but less than 10. However, just to remind us, if we thought that 𝑦 could be in fact eight or 10, then what we’d have to use is an inequality sign with a line underneath it, which means or equal to.

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