You have the following information:
- A is in between Y and Z
- YA = 46
- AZ = 8x
- YZ = 166
In order to find the value of x, you consider that segment YZ is the sum of segments YA and AZ:
[tex]YZ=YA+AZ[/tex]You replace the given esxpressions for each segment:
[tex]166=46+8x[/tex]Then, you solve the previous equation for x. You subtract 46 both sides of the equation, and then you divide both sides by 8, just as follow:
[tex]\begin{gathered} 166=46+8x \\ 166-46=8x \\ 120=8x \\ \frac{120}{8}=x \\ x=15 \end{gathered}[/tex]Hence, the value of x is x = 15
In the image below there is a diagram of the segments:
