Equations with Parentheses, Decimals, & Fractions Quick Check 4 of 54 of 5 Items Question Solve for x in the equation 102.5(x−11.92)=71.6. Round your answer to 3 decimal places.(1 point) Responses 12.618 12.618 0.699 0.699 −11.221 negative 11.221 12.619?

Answer 1

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

1. Distribute the \( 102.5 \) on the left side: \[ 102.5x - 102.5 \times 11.92 = 71.6 \] \[ 102.5x - 1224.6 = 71.6 \]

2. Add \( 1224.6 \) to both sides: \[ 102.5x = 71.6 + 1224.6 \] \[ 102.5x = 1296.2 \]

3. Divide both sides by \( 102.5 \): \[ x = \frac{1296.2}{102.5} \] \[ x \approx 12.61951219512195 \]

4. Round the answer to 3 decimal places: \[ x \approx 12.619 \]

Thus, the answer is 12.619.