To determine how many solutions exist for the equation 3x + 13 = 3x + 6 + 1, we first simplify the equation.
Start by simplifying the right-hand side:
- The right side: 3x + 6 + 1 simplifies to 3x + 7.
Now our equation looks like this:
3x + 13 = 3x + 7
Next, eliminate 3x from both sides of the equation:
- Subtract 3x from both sides:
13 = 7
This statement, 13 = 7, is not true. It indicates there is no value of x that can satisfy the original equation. Therefore, the equation has no solutions.
In conclusion, the equation 3x + 13 = 3x + 6 + 1 has zero solutions.