ShmoopTube

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It's a bird! It's a plane! It's Shmooperman!

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If y equals 2x + z over z + 1, what happens to the value of x when y and z are doubled?

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And here are the potential answers…

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There are three variables, and the question asks what happens to one of them,

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x, if we change the other two, y and z.

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Well, first we should isolate x so that we can see what happens.

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First, we multiply both sides by z + 1, and get y times z + 1 is equal to 2x + z

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Next, we subtract z from both sides so that we can further isolate x.

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Finally, we divide both sides by 2, and x is fully isolated.

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At this point we can plug in test values.

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An easy value is always 1. We can plug in 1 for both y and z.

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And we'll see that x is equal to 1/2.

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What happens when y and z are doubled?

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Well, if we plug in y and z equal 2, we'll get x equals 2 as our answer.

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2 is four times bigger than 1/2 and looks like D is our answer. Done.

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