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### Problem 1:
An electric car can drive 4.2 miles on the highway for every kilowatt-hour (kWh) used by the battery. You are asked to solve for the number of kilowatt-hours used, \( n \), based on the distance traveled \( d \).

The relationship given is:

\[
d = 4.2 \times n
\]

To solve for \( n \) (the number of kilowatt-hours), rearrange the equation:

\[
n = \frac{d}{4.2}
\]

This equation tells you that the number of kilowatt-hours used is equal to the distance traveled divided by 4.2. For every 4.2 miles driven, 1 kilowatt-hour of energy is used.

---

### Problem 2:
Reynaldo plans a 227-mile trip. His car battery can use 47 kWh of energy. The car can travel between 4.3 miles and 4.8 miles for each kWh.

To determine if Reynaldo has enough energy to complete the trip, calculate the total distance he can travel with his battery:

- If the car travels 4.3 miles per kWh:
  \[
  \text{Total distance} = 47 \times 4.3 = 202.1 \text{ miles}
  \]
  
- If the car travels 4.8 miles per kWh:
  \[
  \text{Total distance} = 47 \times 4.8 = 225.6 \text{ miles}
  \]

Reynaldo needs to travel 227 miles, but the maximum range of the car is 225.6 miles, which is just short of the required distance. Therefore, he **won't** have enough energy to complete the trip unless conditions improve to allow for slightly better energy efficiency.

A reasonable rounding choice would be to round distances to the nearest tenth of a mile or kWh, as it's a relatively small difference that could matter in this context.

---

### Problem 3:
The equation given is:

\[
4(x + 4) = \frac{x - 3}{2}
\]

Let’s solve this step by step.

1. **Distribute the 4 on the left-hand side:**
   \[
   4(x + 4) = 4x + 16
   \]
   So, the equation becomes:
   \[
   4x + 16 = \frac{x - 3}{2}
   \]

2. **Multiply both sides of the equation by 2 to eliminate the fraction:**
   \[
   2 \times (4x + 16) = 2 \times \frac{x - 3}{2}
   \]
   This simplifies to:
   \[
   8x + 32 = x - 3
   \]

3. **Move all terms involving \( x \) to one side:**
   \[
   8x - x = -3 - 32
   \]
   Simplifies to:
   \[
   7x = -35
   \]

4. **Solve for \( x \):**
   \[
   x = \frac{-35}{7} = -5
   \]

So, \( x = -5 \).

---

Let me know if you need further details on any of these solutions or concepts!

### 5 Related Questions:
1. What would happen if the car traveled 5 miles per kilowatt-hour instead of 4.8 miles?
2. How can you verify that Reynaldo cannot complete his trip without extra energy?
3. If Reynaldo's trip was 220 miles, how much energy would he need?
4. What are the steps to solve a linear equation with fractions, like in problem 3?
5. How would rounding to a different decimal place change the outcome in problem 2?

### Tip:
Always double-check whether multiplying or dividing by a specific number changes the unit of measurement—this helps avoid errors in problems involving distance, time, or energy.

1. An electric car can drive 4.2 miles on the highway for every kilowatt-hour used by the battery. Solve this equation for n. What does your equation tell you about the number of kilowatt-hours used?
2. Reynaldo plans a 227-mile trip with his electric car. His car battery is charged so he can use 47 kilowatt-hours. Reynaldo's electric car can travel between 4.3 mi and 4.8 mi for every kilowatt-hour used by the battery. Will he have enough kilowatt-hours to complete his trip? What choice in rounding makes sense for this situation?
3. Solve the equation 4(x + 4) = (x - 3) / 2. Justify each step in your solution.

Learn how to solve algebraic equations and energy efficiency problems. This problem covers key concepts like solving linear equations, calculating distance and energy usage, and determining if an electric car has enough energy for a trip. Suitable for students in Grades 8-10.

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