Answer:
[tex]\large \boxed{n = \dfrac{13}{3}; YZ = \dfrac{5}{3}}}[/tex]
Step-by-step explanation:
I think you have the situation shown in the diagram below.
1. Calculate the value of n
[tex]\begin{array}{rcl}XY + YZ & = & XZ\\4n+ 3 + 2n - 7 & = & 22\\6n - 4 & = & 22\\6n & = & 26\\n & = & \dfrac{26}{6}\\\\& = & \mathbf{\dfrac{13}{3}}\\\end{array}\\\large \boxed{\mathbf{n = \dfrac{13}{3}}}[/tex]
2. Calculate the value of YZ
[tex]\begin{array}{rcl}YZ & = & 2n - 7\\& = & 2\left (\dfrac{13}{3}\right ) - 7 \\\\& = & \dfrac{26}{3} - 7\\\\& = & \dfrac{26}{3} - \dfrac{21}{3}\\\\& = & \dfrac{5}{3} \\\\\end{array}\\\large \boxed{YZ = \mathbf{ \dfrac{5}{3}}}[/tex]
