Justify your steps using the properties of equality as you solve for the variable. −5n −2 = −5(4 + 2n) + 8n
Step 1: Distribute the -5 on the right side of the equation:
-5n - 2 = -20 - 10n + 8n
Step 2: Combine like terms:
-5n - 2 = -20 - 2n
Step 3: Add 5n to both sides of the equation to isolate the variable:
-5n + 5n - 2 = -20 - 2n + 5n
-2 = -20 + 3n
Step 4: Add 20 to both sides of the equation to further isolate the variable:
-2 + 20 = -20 + 3n + 20
18 = 3n
Step 5: Divide both sides of the equation by 3 to solve for n:
18/3 = 3n/3
6 = n
Therefore, the solution for the variable n is 6.