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

## $1.5<=<\frac{17}{3}$

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in our diagram, we have one paras sides Markon grunt. We also have a shared side. That is, Congrats, it and they're included. Angles are not congruent. So using the hinge here, um, the side opposite of the largest angle is gonna be your largest, longest side. So Z plus 11 is gonna be greater than the side opposite of the smaller angle. Four Z minus six. Using a little algebra when a subtract ze from both sides and add six to both sides, which gives us 17 as greater than three Z and dividing by three, we get 17/3 is greater than Z. You're five and 2/3 which using mixed fractions. Mixed numbers is not usually what we do, so I would prefer the improper fraction. However, it's not the only condition we need to consider because he is, ah, part of a side measurement. The side of a triangle cannot equal zero any value of Z plus 11. Ah, For any positive number, Z plus 11 is gonna be a greater than zero. We need to take into consideration for Z minus six being smaller than Z plus 11. So this measurement has to be greater than zero. So we're gonna add six to both sides. So we get for Z is greater than six and dividing by four on both sides. We get Z is greater than three halves and I'm gonna leave that three has because we're using an improper fraction and the other inequality. So to sum this up for all values e such that three halves is less than any values e but she is also less than 17 3rd

University of Oklahoma

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