ShmoopTube

00:03

And here's another shmoop du jour.

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The equation ax = 1 can be solved for x using the steps shown below:

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What are some of the properties used to solve this equation?

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And here are the potential answers…

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So… what is this question asking?

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It's asking the basic properties of solving equations... like identity, distributive, and associative.

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Let's refresh our brains on what these properties are...

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The identity property is when any number, a, when multiplied by 1, will get back itself.

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This seems to happen on the right side between steps 2 and 3.

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So looks like we can eliminate choices A and B. Identity has to be in there somewhere.

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The distributive property is when a number, like a, can be distributed...

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…so, for example… a times the quantity b plus c… equals a times b… plus a times c.

01:00

Doesn't look like anything's being distributed... so we can eliminate C.

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Just to make sure, let's review what associative property is.

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Associative property is when we can group terms in any way...and still get the same result.

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It works for addition and multiplication, not subtraction and division.

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Looking at the left side and right side in steps 1 and 2, it looks like the terms 1 over

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a, a, and x are being grouped differently to get the same result.

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So associative and identity are the two properties…

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…looks like our answer is D!

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As in, “Dark Knight Apprises”

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