Let's solve the equation $2x - 4(x - 1) = 10$.

Step 1: Distribute the $-4$ across the terms inside the parentheses

$2x - 4(x - 1) = 2x - 4x + 4$ So, the equation becomes: $2x - 4x + 4 = 10$

Step 2: Combine like terms

$(2x - 4x) + 4 = 10$ $-2x + 4 = 10$

Step 3: Isolate the variable term

Subtract 4 from both sides: $-2x = 10 - 4$ $-2x = 6$

Step 4: Solve for $x$

Divide both sides by $-2$: $x = \frac{6}{-2} = -3$

So, the solution is $x = -3$.

Would you like more details or have any questions?

Here are 8 related questions for further exploration:

1. What would happen if you replaced the constant 10 with a different number in the original equation?
2. How would the solution change if the equation were $2x + 4(x - 1) = 10$?
3. What if the equation was $2x - 4(x + 1) = 10$? How would you solve it?
4. Can you solve $3x - 5(x - 2) = 8$ and compare the steps?
5. What if the original equation had an additional constant, like $2x - 4(x - 1) + 2 = 10$?
6. How do you check if your solution is correct by substituting it back into the original equation?
7. What if you had a similar equation with a quadratic term, like $2x^2 - 4(x - 1) = 10$?
8. How does solving a linear equation differ from solving a system of linear equations?

Tip: Always double-check your solution by substituting it back into the original equation to ensure it's correct!