Question

u is the midpoint of (overline{tv}). if (uv = 8x + 3) and (tv = 17x + 4), what is (tv)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use the mid - point property

Since \(U\) is the midpoint of \(\overline{TV}\), then \(TV = 2UV\).
Given \(UV=8x + 3\) and \(TV = 17x+4\), we substitute into the equation \(TV = 2UV\):
\(17x + 4=2(8x + 3)\)

Step2: Expand and solve for \(x\)

Expand the right - hand side: \(17x + 4=16x+6\).
Subtract \(16x\) from both sides: \(17x-16x + 4=16x-16x + 6\), so \(x+4 = 6\).
Subtract \(4\) from both sides: \(x=6 - 4=2\).

Step3: Find the value of \(TV\)

Substitute \(x = 2\) into the expression for \(TV\): \(TV=17x + 4\).
\(TV=17\times2+4\).
First, calculate \(17\times2 = 34\), then \(34 + 4=38\).

Answer:

\(38\)