Question

question point t is on line segment $overline{su}$. given $su = 5x,tu = 2x$, and $st = 4x - 3$, determine the numerical length of $overline{tu}$. answer attempt 2 out of 2 $tu = 61$

Explanation:

Step1: Use segment - addition postulate

Since point T is on line - segment $\overline{SU}$, we know that $SU=ST + TU$.
Substitute the given expressions: $5x=(4x - 3)+2x$.

Step2: Simplify the right - hand side of the equation

Combine like terms on the right - hand side: $(4x - 3)+2x=4x+2x - 3=6x - 3$. So, the equation becomes $5x=6x - 3$.

Step3: Solve for x

Subtract $5x$ from both sides: $0=6x - 5x-3$.
This simplifies to $x = 3$.

Step4: Find the length of TU

We know that $TU = 2x$. Substitute $x = 3$ into the expression for $TU$.
$TU=2\times3 = 6$.

Answer:

$6$