Question

Solve the equation: -6n + 8(-1 + 2n) = -2(-4n - 2). Show the steps.

Answer 1

To solve the equation -6n + 8(-1 + 2n) = -2(-4n - 2), distribute the numbers inside the parentheses, combine like terms, move variables to one side, constants to the other, simplify, and divide to isolate the variable. The solution is n = 6.

Step-by-step explanation:

To solve the equation -6n + 8(-1 + 2n) = -2(-4n - 2), follow these steps:

1. Distribute the numbers outside the parentheses: -6n + 8(-1) + 8(2n) = -2(-4n) -2(-2).
2. Perform the multiplication: -6n - 8 + 16n = 8n + 4.
3. Combine like terms on each side: -6n + 16n becomes 10n on the left, and 8n on the right side doesn't combine with anything.
4. Rewrite the equation with combined terms: 10n - 8 = 8n + 4.
5. Move all n terms to one side and constants to the other: 10n - 8n = 4 + 8.
6. Simplify both sides: 2n = 12.
7. Divide both sides by 2 to isolate n: n = 6.
8. Check the solution by substituting n = 6 into the original equation to ensure each side is equal.

The solution to the equation is n = 6.