Question

Solve for x
in the equation 102.5(x−11.92)=71.6
. Round your answer to 3 decimal places.(1 point)
Responses

Answer 1

To solve the equation \( 102.5(x - 11.92) = 71.6 \), we can follow these steps:

1. **Distribute the 102.5**:
\[
102.5x - 102.5 \times 11.92 = 71.6
\]

Calculating \( 102.5 \times 11.92 \):
\[
102.5 \times 11.92 = 1223.4
\]
Thus, the equation simplifies to:
\[
102.5x - 1223.4 = 71.6
\]

2. **Add 1223.4 to both sides**:
\[
102.5x = 71.6 + 1223.4
\]
\[
102.5x = 1295
\]

3. **Divide by 102.5** to isolate \( x \):
\[
x = \frac{1295}{102.5}
\]

4. **Calculating the division**:
\[
x = 12.63414634 \ldots
\]

5. **Rounding to 3 decimal places**:
\[
x \approx 12.634
\]

Therefore, the final answer is:
\[
\boxed{12.634}
\]