Answer:
[tex]|tv = 14[/tex]
Step-by-step explanation:
Given
[tex]|tv = x + 10[/tex]
[tex]|tu = 3x - 8[/tex]
[tex]|uv = 10[/tex]
Required
Determine length of tv
Length tv is calculated by adding lengths tu and uv.
In other words
[tex]tv = tu + uv[/tex]
Substitute values for tv, tu and uv
[tex]x + 10 = 3x-8+10[/tex]
Collect like terms
[tex]x - 3x = -8+10 -10[/tex]
[tex]-2x = -8[/tex]
Divide both sides by -2
[tex]x = 4[/tex]
Recall that [tex]|tv = x + 10[/tex]
Substitute 4 for x
[tex]|tv = 4 + 10[/tex]
[tex]|tv = 14[/tex]
Hence, the length of line segment tv is 14
