Let's solve the equation $2x - 3(x + 4) = 3x - 4$.

Step-by-step Solution:

1. Distribute the $-3$ on the left-hand side: $2x - 3(x + 4) = 2x - 3x - 12$ So, the equation becomes: $2x - 3x - 12 = 3x - 4$

2. Combine like terms on the left-hand side: $(2x - 3x) - 12 = 3x - 4$ $-x - 12 = 3x - 4$

3. Move the $x$-terms to one side and constants to the other side. First, add $x$ to both sides: $-12 = 4x - 4$

4. Add 4 to both sides to move the constant on the right-hand side: $-12 + 4 = 4x$ $-8 = 4x$

5. Solve for $x$ by dividing both sides by 4: $x = \frac{-8}{4}$ $x = -2$

Final Answer:

$x = -2$

Do you need any more details or explanations about this solution?

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Here are 5 related questions:

1. What happens if you change the constant term on the right-hand side of the equation?
2. How do you check if $x = -2$ is a solution to the original equation?
3. How would the solution change if the equation had a different coefficient for $x$?
4. What is the general method to solve linear equations with variables on both sides?
5. Can this type of equation have more than one solution?

Tip: Always double-check your solution by substituting it back into the original equation!