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

## $2.5<x<12$

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in our problem. We've got two sides. Mark congruent we have a second side that is a shared side. So it is congruent itself and we've got the included angle in between our congruent sides of the two triangles. However, the included angles are not congruent. So we need to use the hinge here, Um, the hinge here, um, stakes that the side opposite of the larger included angle is going to be greater than the side opposite of the smaller included angle. If we use our algebra steps, I'm going to subtract one X from both sides. That leaves seven is greater than X minus five. Adding five to both sides. I get 12 is greater than X, so we know X has to be smaller than the number 12. However, we also need to take in consideration the smaller of the two sides. It's always gonna be smaller, but it has to be greater than zero. So I also have to consider the two x minus five must be greater than zero. If it's greater than zero, the larger side is also gonna be greater than zero, adding five Both sides I get two X is greater than five and dividing by two. We get X has to be greater than five halves, so our range of X values is all X values such that five halves is are smaller than X, but X is also smaller than 12.

University of Oklahoma

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