Question

What mistake did Carlos make with the steps he took to solve for x? Explain in detail
5x + 7.5 = 25
5x = 32.5
x = 6.5

Answer 1

To solve the equation \(5x + 7.5 = 25\), Carlos made a mistake in the second step of his calculation. Let’s break down the process step-by-step to identify the mistake:

1. **Starting Equation**:
\[
5x + 7.5 = 25
\]

2. **Isolate \(5x\)**:
Carlos should subtract \(7.5\) from both sides of the equation to isolate the term \(5x\):
\[
5x + 7.5 - 7.5 = 25 - 7.5
\]
Thus, the equation simplifies to:
\[
5x = 17.5
\]

3. **Solve for \(x\)**:
Next, Carlos should divide both sides by \(5\) to solve for \(x\):
\[
x = \frac{17.5}{5}
\]
Calculating this gives:
\[
x = 3.5
\]

### Summary of Mistake:
- **Incorrect Calculation of \(5x\)**: Instead of correctly calculating \(5x\) as \(17.5\), Carlos mistakenly wrote \(32.5\) in the step where he isolated \(5x\). This error led to an incorrect value for \(x\).
- **Final Result**: The actual answer for \(x\) is \(3.5\), not \(6.5\) as Carlos concluded.

In summary, Carlos's error was in the subtraction step where he miscalculated \(25 - 7.5\), leading to an incorrect equation for \(5x\).