Question

Solve the equation and check: (n - 3 + n + 5 = 7 × frac{5}{14}).

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution is n = 2.
B. The solution is all real numbers.
C. There is no solution.

Answer 1

The equation is simplified to 2n + 2 = 2.5, which is then solved to find that n = 0.25. The solution is checked and confirmed, however none of the provided choices match the found solution.

Step-by-step explanation:

To solve the equation (n - 3 + n + 5 = 7 × \(\frac{5}{14}\)), we first simplify the left side of the equation by combining like terms (2n + 2) and then simplify the right side by multiplying 7 with the fraction \(\frac{5}{14}\).

Step 1: Combine like terms on the left side:
2n + 2

Step 2: Multiply the fraction on the right side:
7 × \(\frac{5}{14}\) = \(\frac{35}{14}\) = 2.5

Step 3: Set the simplified expressions equal to each other and solve for n:
2n + 2 = 2.5
2n = 2.5 - 2
2n = 0.5
n = \(\frac{0.5}{2}\)
n = 0.25

Step 4: Check the solution by substituting n back into the original equation to ensure the left side equals the right side:

((0.25 - 3) + (0.25 + 5)) = ((-2.75 + 5.25)) = 7 × \(\frac{5}{14}\)
2.5 = 2.5
The check confirms our solution is correct. Thus, none of the provided choices match our solution, indicating there could have been an error in the question, or possibly a mismatch in the provided options and the actual solution.