Question

The following solution is incorrect. Explain the errors then solve it correctly. -8+4(1+5n) = -6n - 14

Answer 1

The given equation is incorrectly solved by the student. The errors are not distributing the 4 and incorrectly stating the sign of 14. The correct solution is n = 9/13.

Step-by-step explanation:

The given equation is: -8 + 4(1 + 5n) = -6n - 14. Let's analyze the solution provided to identify the errors:

1. Incorrect sign in the equation: The solution incorrectly states that there is a -14 on the right side of the equation, but it should be +14.
2. Failure to distribute the 4: The solution does not distribute the 4 to both terms inside the parentheses.

To solve the equation correctly, we need to correct these errors. Here's the step-by-step solution:

1. Apply the distributive property: -8 + 4(1 + 5n) = -8 + 4 + 20n = -4 + 20n
2. Combine like terms: -4 + 20n = -6n + 14
3. Move all terms containing n to one side and constant terms to the other side: 20n + 6n = 14 + 4
4. Combine like terms again: 26n = 18
5. Divide both sides by 26: n = 18/26 = 9/13

Therefore, the correct solution to the equation is n = 9/13.