Question

point u is on line segment $overline{tv}$. given $tv = x + 10$, $tu = 3x - 8$, and $uv = 10$, 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 $TV=TU + UV$. Substituting the given expressions, we get $x + 10=(3x - 8)+10$.

Step2: Simplify the equation

$x + 10=3x - 8+10$ simplifies to $x + 10=3x + 2$.

Step3: Solve for x

Subtract x from both sides: $10 = 3x - x+2$, so $10 = 2x+2$. Then subtract 2 from both sides: $10 - 2=2x$, which gives $8 = 2x$. Divide both sides by 2: $x = 4$.

Step4: Find the length of TV

Substitute $x = 4$ into the expression for TV. Since $TV=x + 10$, then $TV=4 + 10$.

Answer:

14