Question

Point u is on line segment tv given tv = x + 10, tu =3x-8, and Uv = 10 determine the numerical length of tv

Answer 1

`|tv = 14`

Explanation:

Given

`|tv = x + 10`

`|tu = 3x - 8`

`|uv = 10`

Required

Determine length of tv

Length tv is calculated by adding lengths tu and uv.

In other words

`tv = tu + uv`

Substitute values for tv, tu and uv

`x + 10 = 3x-8+10`

Collect like terms

`x - 3x = -8+10 -10`

`-2x = -8`

Divide both sides by -2

`x = 4`

Recall that
`|tv = x + 10`

Substitute 4 for x

`|tv = 4 + 10`

`|tv = 14`

Hence, the length of line segment tv is 14