Equations with Parentheses, Decimals, & Fractions Quick Check

Question

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.