Solve the following equation for x: 2x-3(x+4)=3x-4




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!

Solve the following equation for x: 2x-3(x+4)=3x-4

Learn how to solve the linear equation 2x - 3(x + 4) = 3x - 4 with a detailed step-by-step solution. This problem covers key algebraic concepts, such as using the distributive property and combining like terms. Suitable for students in Grades 7-9.

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