justify your steps using the properties of equality as you solve for the variable. -5n - 2 = -5(4 = 2n) + 8n
To solve for the variable in the given equation -5n - 2 = -5(4 - 2n) + 8n, we will use the properties of equality to simplify the equation step by step.
Step 1: Distribute the -5:
-5n - 2 = -20 + 10n + 8n
Step 2: Combine like terms:
-5n - 2 = -20 + 18n
Step 3: Move the terms containing n to one side by subtracting 18n from both sides:
-5n - 18n - 2 = -20 + 18n - 18n
Simplifying this gives:
-23n - 2 = -20
Step 4: Move the constant term to the other side by adding 2 to both sides:
-23n - 2 + 2 = -20 + 2
Simplifying this gives:
-23n = -18
Step 5: Solve for the variable by dividing both sides by -23:
-23n / -23 = -18 / -23
Simplifying this gives:
n = 18/23
Therefore, the solution to the equation is n = 18/23.