Question

point u is on line segment $overline{tv}$. given $uv = 2$, $tu = 5x$, and $tv = 3x + 6$, determine the numerical length of $overline{tv}$. answer attempt 1 out of 2 tv =

Explanation:

Step1: Use segment - addition postulate

Since point U is on line segment $\overline{TV}$, we have $TU + UV=TV$. Substituting the given values, we get the equation $5x + 2=3x + 6$.

Step2: Solve the equation for x

Subtract $3x$ from both sides: $5x-3x + 2=3x-3x + 6$, which simplifies to $2x+2 = 6$. Then subtract 2 from both sides: $2x+2 - 2=6 - 2$, so $2x=4$. Divide both sides by 2: $\frac{2x}{2}=\frac{4}{2}$, and $x = 2$.

Step3: Find the length of TV

Substitute $x = 2$ into the expression for $TV$. Since $TV=3x + 6$, then $TV=3\times2+6$. First, calculate $3\times2 = 6$, then $6+6=12$.

Answer:

$12$