Final answer:
The equation -4x + 12 = 4x + 20 is solved by combining like terms, moving them to one side of the equation, and then isolating the variable x, giving the solution x = -1.
Step-by-step explanation:
To solve the algebraic equation -4x + 12 = 4x + 20, we must isolate the variable x. Here's a step-by-step solution:
Combine like terms by getting all the x terms on one side and the constants on the other. To do this, add 4x to both sides of the equation:
-4x + 4x + 12 = 4x + 4x + 20, which simplifies to
12 = 8x + 20.
Next, subtract 20 from both sides to get all constants on one side:
12 - 20 = 8x, which simplifies to
-8 = 8x.
Finally, divide both sides by 8 to solve for x:
-8 / 8 = 8x / 8, which gives us
x = -1.