Gathering the x's

In $4x+3 = x+15$, there is an x-term on both sides and a number on both sides. Collect the x-terms first by subtracting $x$ from both sides. Then collect the numbers by subtracting 3 from both sides. Then divide.

$$3x+3 = 15$$

$$3x = 12$$

$$x = 4$$

Check: $4\cdot 4+3 = 19$ and $4+15 = 19$.

You can collect the x-terms on either side. If you collect them on the side with the larger coefficient, the new coefficient is positive. Here the larger coefficient is on the left, so subtract $x$ from both sides to collect the x-terms on the left.