4x How many solutions can be found for the linear equation? $$ 3(x+4)=3 x+4 $$

Question

UpStudy AI · Accepted Answer

To determine how many solutions exist for the linear equation $$ 3(x + 4) = 3x + 4 $$, let's solve it step-by-step.

1. **Expand the Left Side:**
   $$
   3(x + 4) = 3x + 12
   $$
   So, the equation becomes:
   $$
   3x + 12 = 3x + 4
   $$

2. **Subtract $$ 3x $$ from Both Sides:**
   $$
   3x + 12 - 3x = 3x + 4 - 3x
   $$
   Simplifying this gives:
   $$
   12 = 4
   $$

3. **Analyze the Result:**
   The equation simplifies to $$ 12 = 4 $$, which is a **contradiction** and clearly false.

**Conclusion:**
Since the equation leads to a false statement, there are **no solutions** to the equation $$ 3(x + 4) = 3x + 4 $$.

**Answer:**  
There are no solutions; the equation has no valid solution.
There are no solutions to the equation $$ 3(x + 4) = 3x + 4 $$.

4x How many solutions can be found for the linear equation?