Answer
z = -10
Work Step by Step
The equation as written is:
-2(z - 4) - (3z - 2) = -2 - (6z - 2)
We first need to apply the distributive property.
-2z + 8 - 3z + 2 = -2 - 6z + 2
Now we can add/subtract like terms on each side of the equation. We can regroup the terms first. The sign to the left of a term stays with the term.
-2z - 3z + 8 + 2 = -6z - 2 + 2
-5z + 10 = -6z
Now, we can add 6z to both sides of the equation.
-5z + 6z + 10 = -6z + 6z
Completing the arithmetic:
z + 10 = 0
Next, subtract 10 from both sides of the equations.
z + 10 - 10 = 0 - 10
z = -10 (our solution)
Checking the answer, we can substitute z = -10 back into the original equation. Once we do this and simplify both sides, we can check to see if the end result matches. If it does, our solution is correct.
-2(z - 4) - (3z - 2) = -2 - (6z - 2)
Substituting -10 for z, we get:
-2(-10 - 4) - [(3)(-10) - 2] = -2 - [(6)(-10) - 2]
Complete operations inside grouping symbols (if more than one operation is inside grouping, use order of operation --it may take more than one step)
-2(-14) - (-30 - 2) = -2 -(-60 - 2)
Keep working in grouping.
-2(-14) - (-32) = -2 - (-62)
Now, multiply left to right
28 + 32 = -2 + 62
Now we add.subtract on each side of the equation.
60 = 60
The answers match, so our solution of z = -10 is correct.
