Answer: The equation that has the same solution as the given equation is −1 − 22 n = −20 n − 9. This can be seen by solving both equations for n.
To solve the given equation − 5 n + 31 = − 14 n − 5 for n, we can start by adding 5n to both sides to obtain 31 = − 9 n − 5. Then, we can add 9n and 5 to both sides to obtain n = −1.
To solve the equation −1 − 22 n = −20 n − 9 for n, we can start by adding 22n to both sides to obtain −1 = −20 n − 9. Then, we can add 20n and 9 to both sides to obtain n = −1.
Since both equations have the same solution for n (namely, n = −1), they have the same solution. Note that the other equations listed in the question do not have the same solution as the given equation. For example, the equation 1 = 0.75 n + 3.25 has the solution n = −4, while the equation 3 − 6 n + 3 n = − 3 + 4 − 4 n has the solution n = 1/5. These solutions are different from the solution n = −1 of the given equation, so these equations do not have the same solution as the given equation.