Answer:
[tex]x=6[/tex]
Step-by-step explanation:
Given:
[tex]AB=3x-1\\XZ=34\\[/tex]
Here , A is the midpoint of XY and B is the midpoint of YZ.
Thus, we can say that AB is one-half of XZ.
To solve for x using the midpoint segment theorem, we have:
[tex]AB=\frac{1}{2} *XZ\\3x-1=\frac{1}{2}*34[/tex]
Let's solve for x:
[tex]3x-1=17\\[/tex]
Add 1 to both sides:
[tex]3x-1+1=17+1\\3x=18[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3} = \frac{18}{3} \\\\x=6[/tex]
Answer: [tex]x=6[/tex]
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