Let's solve the equation \(6x - 2 = 1 - (8x - 4)\).

### Step 1: Simplify the right-hand side
Distribute the negative sign across the parentheses on the right-hand side:
\[
6x - 2 = 1 - 8x + 4
\]

Now combine the like terms on the right-hand side:
\[
6x - 2 = -8x + 5
\]

### Step 2: Move all terms involving \(x\) to one side
Add \(8x\) to both sides to move the \(x\) terms to the left-hand side:
\[
6x + 8x - 2 = 5
\]
\[
14x - 2 = 5
\]

### Step 3: Move the constant term to the other side
Add \(2\) to both sides to isolate the term with \(x\):
\[
14x = 5 + 2
\]
\[
14x = 7
\]

### Step 4: Solve for \(x\)
Divide both sides by \(14\) to isolate \(x\):
\[
x = \frac{7}{14}
\]
\[
x = \frac{1}{2}
\]

The solution is \(x = \frac{1}{2}\).

Would you like more details or have any questions?

Here are some related questions:
1. What if the equation was \(6x - 2 = 2 - (8x - 4)\)? How would the solution change?
2. How can you verify the solution to this equation?
3. What if there was a different coefficient in front of \(x\) on both sides?
4. Can you explain how to solve an equation where both sides are quadratic?
5. How would this problem change if the equation included fractions?

**Tip:** When dealing with negative signs in front of parentheses, distribute carefully to avoid sign errors.

Learn how to solve the equation 6x - 2 = 1 - (8x - 4) step-by-step with a detailed solution. This problem covers key algebraic concepts, including equations, distributive property, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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