Answer:
[tex]XZ=146[/tex]
Step-by-step explanation:
Since [tex]M[/tex] is the midpoint of segment [tex]XZ[/tex]:
[tex]XM+MZ=XZ[/tex]
[tex]XM=MZ[/tex]
Identify your known values:
[tex]XM=2x+35\\MZ=5x-22\\[/tex]
Solve for [tex]x[/tex]:
[tex]2x+35=5x-22[/tex]
Subtract [tex]35[/tex] from both sides of the equation:
[tex]2x=5x-57[/tex]
Subtract [tex]5x[/tex] from both sides of the equation:
[tex]-3x=-57[/tex]
Divide by the coefficient of [tex]x[/tex], which is [tex]-3[/tex]:
[tex]x=19[/tex]
Substitute:
[tex]XM=2(19)+35\\MZ=5(19)-22[/tex]
Solve:
[tex]XM=73\\MZ=73[/tex]
Again, we know:
[tex]XM+MZ=XZ[/tex]
Therefore:
[tex]XZ=73+73[/tex]
Solve:
[tex]XZ=146[/tex]
