Question: For a show during the half-time break of a football game, a stage will be set up on the field. The center of the stage is on the 35-yard line. If the distance from the center to the outer edges is 11 yards, which equation can be used to find the locations of the outer edges of the stage?
A |x − 35| = 11
B |x − 11| = 35
C 2|x − 35| = 11
D 2|x − 11| = 35
1. **State the problem:** We need to find an equation that represents the locations of the outer edges of a stage centered at the 35-yard line, with the distance from the center to each edge being 11 yards.
2. **Understand the concept:** The center of the stage is at $x = 35$. The outer edges are 11 yards away from this center, so the distance from $x$ to 35 is 11.
3. **Use the distance formula on a number line:** The distance between $x$ and 35 is given by the absolute value $|x - 35|$.
4. **Set up the equation:** Since the distance is 11 yards, the equation is:
$$|x - 35| = 11$$
5. **Check the options:**
- Option A: $|x - 35| = 11$ matches our equation.
- Option B: $|x - 11| = 35$ is incorrect because the center is 35, not 11.
- Option C: $2|x - 35| = 11$ is incorrect because the distance is not doubled.
- Option D: $2|x - 11| = 35$ is incorrect for the same reasons.
**Final answer:** Option A
The equation that can be used to find the locations of the outer edges of the stage is:
$$|x - 35| = 11$$