Question: Point T is on line segment SU. Given $ST = 2x - 1$, $SU = 2x + 4$, and $TU = 2x - 7$, determine the numerical length of $SU$.
1. **State the problem:** We need to find the numerical length of the segment $SU$ given expressions for $ST$, $SU$, and $TU$.
2. **Recall the segment addition postulate:** If point $T$ lies on segment $SU$, then $ST + TU = SU$.
3. **Write the equation using given expressions:**
$$ (2x - 1) + (2x - 7) = 2x + 4 $$
4. **Simplify the left side:**
$$ 2x - 1 + 2x - 7 = 4x - 8 $$
5. **Set up the equation:**
$$ 4x - 8 = 2x + 4 $$
6. **Solve for $x$:**
Subtract $2x$ from both sides:
$$ \cancel{4x} - 8 = \cancel{2x} + 4 \Rightarrow 2x - 8 = 4 $$
Add $8$ to both sides:
$$ 2x - \cancel{8} + 8 = 4 + 8 \Rightarrow 2x = 12 $$
Divide both sides by $2$:
$$ \frac{2x}{\cancel{2}} = \frac{12}{\cancel{2}} \Rightarrow x = 6 $$
7. **Find the length of $SU$ by substituting $x=6$ into $SU = 2x + 4$:**
$$ SU = 2(6) + 4 = 12 + 4 = 16 $$
**Final answer:** The length of $SU$ is $16$.