Solve for n

Question

in the equation 50.3(n+9.25)=−120.72
.(1 point)
Responses

6.85
6.85

−2.4
negative 2.4

−6.85
negative 6.85

−11.65

Answer 1

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

1. Distribute the \( 50.3 \): \[ 50.3n + 50.3 \times 9.25 = -120.72 \] First, calculate \( 50.3 \times 9.25 \): \[ 50.3 \times 9.25 = 465.775 \] So, the equation becomes: \[ 50.3n + 465.775 = -120.72 \]

2. Isolate \( 50.3n \) by subtracting \( 465.775 \) from both sides: \[ 50.3n = -120.72 - 465.775 \] Calculate the right side: \[ -120.72 - 465.775 = -586.495 \] So the equation is now: \[ 50.3n = -586.495 \]

3. Solve for \( n \) by dividing both sides by \( 50.3 \): \[ n = \frac{-586.495}{50.3} \] Now calculate the division: \[ n \approx -11.65 \]

Thus, the solution for \( n \) is: \[ \boxed{-11.65} \]