To determine how many solutions exist for the equation 3x + 10 = 6 + 3x + 12, we first rearrange the equation to isolate x.
Starting with the original equation:
3x + 10 = 6 + 3x + 12
We can simplify the right side:
6 + 12 = 18
Now the equation looks like this:
3x + 10 = 3x + 18
If we subtract 3x from both sides:
10 = 18
This statement is clearly false; 10 is not equal to 18. This tells us that there are no values of x that can satisfy the equation.
Thus, the conclusion is that there are no solutions for the given equation.