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

## $$1.2<x<3$$

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we can see we have two triangles with a corresponding side that is congratulated. They also have a shared side, which makes that can grew int, and we have an included angle in between the corresponding sides. However, our included angles or not congruent hinge there. Um, states, if you know the angle measurements, the angle opposite of the smaller or the side opposite of the smaller angle is going to be less than the side opposite of the larger angle. So that gives us an algebraic equation of five. X minus six has to be less than nine using our algebra steps. If I add six to both sides, I get five. X is less than 15 and dividing by five we get X is less than three. But that's not the only thing we want to take into consideration. Five X minus six is the side of a triangle. It cannot be zero. It can't be less than zero. So we have another condition that says five X minus six must also be greater than zero to be the side of a triangle. So again, using our algebra steps, I'm gonna add six to both sides, giving us five x is greater than six, dividing by five on both sides. We get X is greater than 6/5 so four X is greater than 1.2. This gives us a range of values for X for any X such that the smallest values 1.2 is less than are any X value, and that also has to be less than three. So any X value between 1.2 and three.

University of Oklahoma

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