Question

point v is on line segment $overline{uw}$. given $vw=x + 7$, $uw = 3x-9$, and $uv = 8$, determine the numerical length of $overline{uw}$. answer attempt 1 out of 2 $uw=$

Explanation:

Step1: Use segment - addition postulate

Since point V is on line segment $\overline{UW}$, we know that $UV + VW=UW$.
Substitute the given expressions: $8+(x + 7)=3x-9$.

Step2: Simplify the left - hand side of the equation

$8+x + 7=3x-9$, which simplifies to $x + 15=3x-9$.

Step3: Solve for x

Subtract x from both sides: $15=3x - x-9$.
$15 = 2x-9$.
Add 9 to both sides: $15 + 9=2x$, so $24=2x$.
Divide both sides by 2: $x = 12$.

Step4: Find the length of UW

Substitute $x = 12$ into the expression for UW.
$UW=3x-9$.
$UW=3\times12-9$.
$UW = 36-9$.
$UW = 27$.

Answer:

$27$