The equation we need to analyze is:
3x + 6 = 1 + 3 + 4x
First, let’s simplify the right side of the equation. Combining the constants gives us:
3x + 6 = 4 + 4x
Next, we want to get all the terms involving x on one side of the equation. To do this, we can subtract 4x from both sides:
3x - 4x + 6 = 4
This simplifies to:
-x + 6 = 4
Now, we will isolate x by subtracting 6 from both sides:
-x = 4 - 6
Which results in:
-x = -2
Finally, multiplying both sides by -1, we get:
x = 2
Thus, the equation has exactly one solution: x = 2. In summary, the equation 3x + 6 = 1 + 3 + 4x has a single solution, and that solution is x = 2.