How many solutions can be found for the linear equation?

3(x + 4) = 3x + 4

Let's solve the linear equation \(3(x + 4) = 3x + 4\) and determine how many solutions it has.

### Step 1: Distribute on the left side
Distribute the 3 on the left-hand side:
\[
3 \times (x + 4) = 3x + 12
\]
So the equation becomes:
\[
3x + 12 = 3x + 4
\]

### Step 2: Subtract \(3x\) from both sides
To simplify the equation, subtract \(3x\) from both sides:
\[
3x + 12 - 3x = 3x + 4 - 3x
\]
This simplifies to:
\[
12 = 4
\]

### Conclusion
The statement \(12 = 4\) is false. Therefore, there is no value of \(x\) that can satisfy this equation. 

**Answer:** The equation has **no solutions**.

Would you like more details or have any questions?

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Here are some related questions to explore further:
1. What does it mean for a linear equation to have no solutions?
2. How would the solution change if the equation were \(3(x + 4) = 3x + 12\)?
3. Can a linear equation have infinitely many solutions? Provide an example.
4. What are the different types of solutions that a linear equation can have?
5. How can you determine the number of solutions of a linear equation without solving it?
6. What happens if we have an equation like \(3(x + 4) = 3(x + 4)\)?
7. How do you solve a linear equation with fractions, like \(\frac{2x + 3}{4} = x - 1\)?
8. What is the graphical interpretation of a linear equation with no solutions?

**Tip:** When the variables cancel out and you're left with a false statement, the equation has no solutions.

Learn how to solve the linear equation 3(x + 4) = 3x + 4 step-by-step with detailed explanations. This problem involves linear equations and the distributive property. Suitable for students in Grades 7-9.

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