ShmoopTube

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For a good time, solve this shmoopy question.

00:05

Solve the inequalities and choose the correct graph: -4 ≤ 2y + 2 < 8.

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And here are your potential options...

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For starters, let's break this into 2 problems.

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We'll start by lopping off 8 at the end there and just consider:

00:22

Negative 4 is less than or equal to 2y plus 2.

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We subtract 2 from both sides to get:

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Negative 6 is less than or equal to 2y.

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Then we divide both sides by 2 to get:

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Negative 3 is less than or equal to y.

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So...let's put this part on the graph...

00:40

We start here at negative 3 ... and y is greater than or equal to this number so we're going

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to move to the right...

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And suddenly, we can eliminate B and D. Note that D has an open circle over negative 3...

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...meaning that it's NOT equal to it but only greater than 3.

00:54

For our equation, it's greater than or equal... so the answer has to be A, C or E.

01:00

OK now consider the second part of the equation separately:

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2y plus 2 is less than 8...

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Subtract 2 from both sides and we have:

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2y is less than 6.

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Divide both sides by 2 and y is less than 3.

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So let's put this part on the graph - and note that we need the open circle above

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positive 3 here because it's not equal to it...

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So the area we're talking about is between here and here.

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Only A works and that's pretty much it.

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