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# Find the range of values for $x .$(FIGURE CANNOT COPY)

## $-4<x<8.5$

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we need to find all possible values for X in two triangles where we have one side corresponding and marking group. And again we have a shared a common side. So the angles that we're comparing are the included angles. Well, the angle opposite of the larger side is gonna be your larger angle. So that makes two X plus eight opposite of the side mark seven, as are smaller angle. But we also need to take in consideration. Any angle measurement must be greater than zero to be in a triangle. So to begin with, we're gonna look for all possible X values. That gives us two X Plus eight as an angle measure less than 25. That's comparing the two angles algebra steps. If I subtract eight from both sides, that leaves me to X, is less than 17 and dividing by two. I get X has to be less than 17 halves, or we could say 17 halves is 8.5, so we know X has to be less than 8.5. Then we need to take into consideration the other situation, and that is the angle Measurement two X plus eight has to be greater than zero. So using our algebra steps subtracting eight from both sides, I have two. X is greater than negative eight and dividing by two, we get X needs to be greater than negative four now. Because X is not a single measurement, it is possible that X can represent a negative number. So to write the value of our range, we're looking for all X such that negative four is less than X and X is less than 8.5 or 17 halves.

University of Oklahoma

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