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

Question

Responses

0.699
0.699

12.619
12.619

−11.221
negative 11.221

12.618

Answer 1

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

1. Distribute the 102.5: \[ 102.5x - 102.5 \times 11.92 = 71.6 \] First, calculate \( 102.5 \times 11.92 \): \[ 102.5 \times 11.92 = 1224.9 \] Therefore, the equation becomes: \[ 102.5x - 1224.9 = 71.6 \]

2. Add 1224.9 to both sides: \[ 102.5x = 71.6 + 1224.9 \] Calculate the right side: \[ 71.6 + 1224.9 = 1296.5 \] So we have: \[ 102.5x = 1296.5 \]

3. Divide both sides by 102.5: \[ x = \frac{1296.5}{102.5} \] Calculate the division: \[ x \approx 12.634146 \]

4. Round to three decimal places: \[ x \approx 12.634 \]

Thus, the correct rounded answer (though not indicated in your choices) is \( 12.634 \). However, looking at the provided options, the closest answer is:

\[ \text{12.619} \]

This might have stemmed from a slightly different calculation approach. However, from the original equation's resolution, \( 12.634 \) is correct.