Question

Equations with Parentheses, Decimals, & Fractions Quick Check
Solve for x in the equation 102.5 (x — 11.92) = 71.6. Round your answer to 3 decimal places.
—11.221
12.619
12.618
0.699

Answer 1

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

1. **Divide both sides by 102.5**:
\[
x - 11.92 = \frac{71.6}{102.5}
\]
Calculate the right-hand side:
\[
\frac{71.6}{102.5} \approx 0.6983
\]

2. **Add 11.92 to both sides**:
\[
x = 0.6983 + 11.92
\]
Calculate the right-hand side:
\[
x \approx 12.6183
\]

3. **Round to three decimal places**:
\[
x \approx 12.618
\]

Thus, the answer is **12.618**.