using inverse operations to solve 2/3n - 6 = -8 show all steps for getting the variable by itself then check your answer by plugging it back into the original equations

Answer 1

To solve the equation 2/3n - 6 = -8 using inverse operations, we need to isolate the variable n.

Step 1: Add 6 to both sides of the equation to eliminate the term -6 on the left side:
2/3n - 6 + 6 = -8 + 6
2/3n = -2

Step 2: To eliminate the coefficient 2/3 in front of n, we need to multiply both sides of the equation by its reciprocal, which is 3/2:
(3/2) * (2/3n) = (3/2) * (-2)
(3 * 2)/(2 * 3) * n = -6/2
6/6 * n = -3
n = -3

The solution to the equation is n = -3.

Now let's check the answer by substituting it back into the original equation:
2/3(-3) - 6 = -8
-6/3 - 6 = -8
-2 - 6 = -8
-8 = -8

Since both sides of the equation are equal, the solution n = -3 is correct.