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Introduction to Real Numbers - Problem 2

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We’re talking about inequalities. Inequalities are essentially symbols that represent statements, like less than, greater than, less than or equal to, greater than or equal to or simply equal to. Let's take a look at some examples.

Here we’ve got 3 and 7. Well 7 is bigger than 3 and you might remember this from elementary school. You want to point that crocodile mouth towards the bigger number. This reads as 3 is less than 7. Here we’ve got 2 and negative 4. Again, crocodile mouth towards the bigger number, and this reads as 2 is greater than negative 4. 5 and 5, well that’s obvious 5 is equal to 5.

We’ve talked about these three, but what about less than or equal to or greater than or equal to? Let’s go over here and look at an inequality. This inequality says that, 3x is less than or equal to 6, and we solve this just like we would any other inequality. Divide both sides by 3 and we’re left with x is less than or equal to 2. What this means is that x can equal 2 or a number smaller than 2, like zero or 1. If we wrote it like this, x is less than 2, x could not equal 2. It could be 1.8, it could be 1.3 but it can’t be 2 because there is no equals 2 sign.

If you just remember the crocodile, you’ll do just fine on these basic inequality problems.

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