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could you help me by explaning how to solve

To solve the problem, we need to calculate the total distance Bryan walks, including the trip from the library (point A) to the soccer field (point C), to the supermarket, and back to the soccer field.

### Step-by-step explanation:

1. **Determine the distance from the library (A) to the soccer field (C):**
   - The distance from A (Library) to C (Soccer Field) is broken into two parts:
     - From A to B (Supermarket), the distance is given as \(5x - 3\) meters.
     - From B to C, the distance is \(2x + 6\) meters.
   - So, the total distance from A to C (one-way trip) is:
     \[
     (5x - 3) + (2x + 6) = 7x + 3 \text{ meters}.
     \]

2. **Determine the total distance Bryan walks:**
   - First, Bryan walks from the library (A) to the soccer field (C), which is \(7x + 3\) meters.
   - After the first soccer game, he walks from the soccer field (C) to the supermarket (B). The distance from C to B is \(2x + 6\) meters.
   - Finally, he walks back from the supermarket (B) to the soccer field (C), which is also \(2x + 6\) meters.

3. **Add up all the distances:**
   - The total distance Bryan walks is the sum of:
     1. From A to C: \(7x + 3\),
     2. From C to B: \(2x + 6\),
     3. From B back to C: \(2x + 6\).

   Therefore, the total distance is:
   \[
   (7x + 3) + (2x + 6) + (2x + 6) = 7x + 3 + 2x + 6 + 2x + 6 = 11x + 15 \text{ meters}.
   \]

Thus, the total distance Bryan walks is \(11x + 15\) meters.

Let me know if you need further clarification on this, or if you'd like to go deeper into the solution!

### Related Questions:
1. If \(x = 3\), what is the total distance Bryan walks?
2. How does the distance change if the supermarket is closer to the library?
3. What is the walking distance if Bryan only walks from A to B and back to A?
4. How could you calculate the total time Bryan spends walking, given his walking speed?
5. If Bryan decided to skip the trip to the supermarket, what would the total distance be?

### Tip:
Always break down multi-step distance problems into individual segments and sum them up carefully to avoid missing any part of the journey.

Bryan is at the library doing a research paper. He leaves the library at point A and walks to the soccer field for a game at point C. The supermarket at point B is exactly halfway between the library and the soccer field. After Bryan's first soccer game, he walks to the supermarket to buy a snack, and then he walks back to the soccer field for his second game. Not including the time spent at the soccer game, how far does Bryan walk?

Solve a multi-step algebra problem where Bryan walks between a library, supermarket, and soccer field. Learn how to calculate the total distance using algebraic expressions and sum individual distances. Suitable for Grade 8 students.

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