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Multi-Step In $\triangle X Y Z, X Z=5 x+15, X Y=8 x-6$ and $\mathrm{m} \angle \mathrm{XVZ}>\mathrm{m} \angle \mathrm{XVY}$. Find the range of values for $x$

(FIGURE CANNOT COPY)

$\frac{3}{4}<x<7$

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given Triangle, X, Y Z and an Interior Point V. We need to find all possible values for X so that the measurement of XY is five X plus 15. The measurement of X Y is eight x minus six, and we know that the measurement of X Veazey that would be this angle here is greater than the measurement of angle XV y, which is this ankle here. So hinge there. Um says that the side opposite of the larger angle is going to be a longer measure, which makes five X plus 15 greater than our smaller angle, which is opposite of the smaller length. So that's a X minus six that taking some algebra steps, I'm going to subtract five x from both sides, which means I'm gonna add six to both sides. Giving me 21 is greater than three X, dividing by three on both sides. I get seven is greater than X, and that's the same thing is saying X is less than seven. But we also have to take into consideration that our smallest measurement has to be greater than zero. If it's greater than zero, the longer measurements gonna be longer than whatever eight X minus six is so we have to take into consideration that eight X minus six must be greater than zero. So if I had six to both signs and divide by eight on both sides, I get X has to be greater than 3/4. So all possible X values, such that 3/4 is the smallest X is greater than 3/4 but X is also less than seven.