Answer:
PT=57
Explanation:
If PT=7x+8 and TQ=9x-6 qnd we have that T is the midpoint of PQ.
Since T is the midpoint of PQ,
![PT=TQ](https://img.qammunity.org/2021/formulas/mathematics/middle-school/6r5w78ea995lehtz8zc6o2izkegj1qkn8p.png)
We substitute into the equation to get:
![7x+8=9x-6](https://img.qammunity.org/2021/formulas/mathematics/middle-school/yxlzce3208aqhsku4n42s0v5el0a1c12g9.png)
Group the similar terms to get:
![8+6=9x-7x](https://img.qammunity.org/2021/formulas/mathematics/middle-school/9q6ar45cow2nc3s8pe0zx95jr98g2dtheu.png)
We simplify now to get:
![14=2x](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qpl8tosivo2gmd7k5jtgfnvxlkbbrkjc5a.png)
Divide through by 2 to get:
![x=7](https://img.qammunity.org/2021/formulas/mathematics/high-school/2bnkqxj7yd0fo7vi8japxxe1irbgu1f8vb.png)
PT=7*7+8=49+8=57