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

Question

(1 point)
0.699
12.618
12.619
−11.221

Answer 1

To solve the equation \( 102.5(x - 11.92) = 71.6 \), start by isolating \( x \).

1. Divide both sides by 102.5:

\[ x - 11.92 = \frac{71.6}{102.5} \]

2. Calculate \( \frac{71.6}{102.5} \):

\[ \frac{71.6}{102.5} \approx 0.6985 \]

3. Now, simplify:

\[ x - 11.92 \approx 0.6985 \]

4. Add \( 11.92 \) to both sides:

\[ x \approx 0.6985 + 11.92 \]

5. Compute the sum:

\[ x \approx 12.6185 \]

6. Round to three decimal places:

\[ x \approx 12.619 \]

Thus, the solution for \( x \) is 12.619.

Answer 2

Solve for n in the equation 50.3(n + 9.25) = − 120.72. (1 point)
−6.85
6.85
−11.65
−2.4

Answer 3

To solve for \( n \) in the equation \( 50.3(n + 9.25) = -120.72 \), follow these steps:

1. Divide both sides by \( 50.3 \):

\[ n + 9.25 = \frac{-120.72}{50.3} \]

2. Calculate \( \frac{-120.72}{50.3} \):

\[ \frac{-120.72}{50.3} \approx -2.398 \]

3. Now simplify the equation:

\[ n + 9.25 \approx -2.398 \]

4. Subtract \( 9.25 \) from both sides:

\[ n \approx -2.398 - 9.25 \]

5. Calculate the right side:

\[ n \approx -11.648 \]

Rounded to two decimal places, this is approximately \( -11.65 \).

Thus, the solution for \( n \) is -11.65.