Need algebra help with writing a compound inequality given a graph on the number line

Anonymous
timer Asked: Dec 21st, 2015
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mallorydyer
School: UCLA

Thank you for the opportunity to help you with your question!

The first part has the line going to the left, meaning x is getting smaller and smaller. Since there is an arrow on the left, that means x is going all the way to negative infinity. Then it stops at x=-2 and notice there is a closed circler there. This means x is <= -2 (x is less than or equal to -2).

The second part has the line going to the right, meaning x is getting bigger and bigger. Since there is an arrow on the end of it, this means x is going all the way to positive infinity. Notice there is a break in the graph and it does not start again until x=1. However, there is an open circle at x=1 so this means x is >1 (x is greater than 1). 

Now we put both together to write the compound inequality. Since these do not overlap and there is a break between the two, we will have two pieces to our answer and it is an OR problem (meaning a union). So the final answer is:

x<= -2 or x>1

set notation {x|x<=-2 U x>1}

interval notation (-infinity,-2] U (1,infinity)

*note ALWAYS use parenthesis around -infinity and infinity

*there is a bracket around -2 because it is included with a closed circle and a parenthesis around 1 because it is not included with an open circle.

I hope this helps!

Mallory : )

Please let me know if you need any clarification. I'm always happy to answer your questions.

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Anonymous
awesome work thanks

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