ShmoopTube

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And here's your shmoop du jour...

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Solve the inequality and determine which solution is shown on the number line

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Y minus two times the quantity Y plus two is less than six

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And here are your options...

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Well anytime we see a number

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right next to a parentheses think distributive property.

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We can think of the -2 as a negative 2

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so distributing we get negative two times Y

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or -2y plus -2 times 2

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or -4 so simplified we have y - 2y - 4 is less than six

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we can combine like terms: y - 2y gives us negative y

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add 4 to both sides and we get negative y is less than 10.

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Now all we have to do is divide by both sides by -1

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Remember that whenever we divide or multiply by negative one with

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inequalities we have to flip the inequality

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So we're left with y is greater than -10

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The inequality is a greater than not a greater than

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or equal to, so that clues us and that we need an

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open dot which immediately eliminates A and B

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We also know that are open dot has to be on -10

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so we can eliminate D and E which leaves us with just C

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and just make sure the arrow is pointing the right way we know that y has to be

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greater than -10

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The arrow points in the positive direction which is greater than -10

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Looks like C is our answer.

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