Solving the Equation: 6x + 2(1 + x) = 3x - 8 + x - 2
In this article, we will solve the equation 6x + 2(1 + x) = 3x - 8 + x - 2. This equation involves combining like terms, distributing the 2 to the terms inside the parentheses, and then solving for x.
Step 1: Distribute the 2
First, we need to distribute the 2 to the terms inside the parentheses:
6x + 2(1 + x) = 6x + 2 + 2x
Step 2: Combine Like Terms
Next, we combine like terms on the left-hand side of the equation:
6x + 2 + 2x = 8x + 2
Step 3: Simplify the Right-Hand Side
Now, let's simplify the right-hand side of the equation:
3x - 8 + x - 2 = 3x + x - 8 - 2 = 4x - 10
Step 4: Equate and Solve
Now we can equate the two expressions:
8x + 2 = 4x - 10
Subtract 2 from both sides:
8x = 4x - 12
Subtract 4x from both sides:
4x = -12
Divide both sides by 4:
x = -12/4 = -3
Therefore, the solution to the equation 6x + 2(1 + x) = 3x - 8 + x - 2 is x = -3.
