Question

You have a group project please answer this question with the real life situation built into it to fit the following equation. Then, solve the equation in two different ways. And Show all the steps. Finally, choose which solution method you liked best and explain your reason. 8(x+9)=144

Answer 1

can you show the steps for the second method

Answer 2

Let's create a real-life situation that fits the equation \(8(x + 9) = 144\).

### Real-Life Situation:
Imagine a school is organizing a fundraising event where they sell tickets for an art show. The school has a fixed cost of $9 for each ticket to cover the materials and refreshments. They have set a goal to raise a total of $144 from ticket sales. There is an additional factor where each ticket is sold at a price represented by \(x\).

The equation \(8(x + 9) = 144\) represents this situation, where \(x + 9\) is the total cost per ticket (including the fixed cost), and \(8\) is the total number of tickets sold.

### Solve the Equation:
1. **Identify the Equation**:
\[ 8(x + 9) = 144 \]

2. **Distribute**:
Multiply \(8\) by both \(x\) and \(9\):
\[ 8x + 72 = 144 \]

3. **Subtract 72 from both sides**:
\[ 8x + 72 - 72 = 144 - 72 \]
\[ 8x = 72 \]

4. **Divide both sides by 8**:
\[ x = \frac{72}{8} \]
\[ x = 9 \]

**First Method Summary**:
- Distribute, combine like terms, isolate \(x\).
- Solution: \(x = 9\)

### Second Method: Reverse Operations
1. **Starting from the original equation**:
\[ 8(x + 9) = 144 \]

2. **Divide both sides by 8**:
\[ x + 9 = \frac{144}{8} \]
\[ x + 9 = 18 \]

3. **Subtract 9 from both sides**:
\[ x + 9 - 9 = 18 - 9 \]
\[ x = 9 \]

**Second Method Summary**:
- Simplified by dividing by 8 first, then isolating \(x\).
- Solution: \(x = 9\)

### Comparison of Methods:
I preferred the **second method** (reverse operations) as my solution technique. The reason is that dividing first simplifies the equation right away, making it less cumbersome to deal with large numbers. I feel this approach makes it easier to visualize the relationship between the components of the equation without needing to distribute first. Overall, both methods yield the correct answer, but the second method feels more straightforward and efficient in this case.

Answer 3

Certainly! Let's break down the second method (reverse operations) step-by-step to solve the equation \(8(x + 9) = 144\).

### Step-by-Step Solution Using Reverse Operations

1. **Start with the original equation**:
\[
8(x + 9) = 144
\]

2. **Divide both sides by 8**:
To simplify the equation, divide both sides by 8 to eliminate the coefficient.
\[
\frac{8(x + 9)}{8} = \frac{144}{8}
\]
This simplifies to:
\[
x + 9 = 18
\]

3. **Subtract 9 from both sides**:
Now, isolate \(x\) by subtracting 9 from both sides.
\[
x + 9 - 9 = 18 - 9
\]
This simplifies to:
\[
x = 9
\]

### Conclusion
When using the reverse operations method, we successfully solved the equation:
\[
x = 9
\]

This method effectively reduced the equation early on, leading to a straightforward path to the solution.