Given:
TW=120
TV=3x+1
UV=x-6
UW=8x-4
The objective is to find the length of UV,
The length of UV can be calculated as,
[tex]\begin{gathered} TW=TV+UW-UV \\ 120=3x+1+8x-4-(x-6) \\ 120=3x+1+8x-4-x+6 \\ 120=10x+3 \\ 10x=120-3 \\ x=\frac{117}{10} \\ x=11.7 \end{gathered}[/tex]
Now, substitute the value of x in UV.
[tex]\begin{gathered} UV=x-6 \\ UV=11.7-6 \\ UV=5.7 \end{gathered}[/tex]
Hence, the length of UV is 5.7.
