Question: 10. Solve for $x$.
F •——— $2x - 10$ ———• G———• H
$2x - 16$
<——— 10 ———>
1. **State the problem:** We need to solve for $x$ given the distances between points F, G, and H, and the total distance of 10 units.
2. **Understand the setup:** The segment from F to G is divided into two parts: $2x - 10$ and $2x - 16$. The total distance from F to H is 10.
3. **Write the equation:** The sum of the two parts equals the total distance:
$$ (2x - 10) + (2x - 16) = 10 $$
4. **Simplify the equation:**
$$ 2x - 10 + 2x - 16 = 10 $$
$$ 4x - 26 = 10 $$
5. **Isolate $x$:**
$$ 4x = 10 + 26 $$
$$ 4x = 36 $$
6. **Divide both sides by 4:**
$$ x = \frac{36}{4} $$
$$ x = 9 $$
7. **Check the solution:**
Calculate each segment:
$$ 2x - 10 = 2(9) - 10 = 18 - 10 = 8 $$
$$ 2x - 16 = 2(9) - 16 = 18 - 16 = 2 $$
Sum:
$$ 8 + 2 = 10 $$
The sum matches the total distance, so $x=9$ is correct.