1. We are asked to solve the equation: $$6x - 2 + x = 2x + 3$$ 2. Combine like terms on the left side: $$6x + x - 2 = 2x + 3$$ $$7x - 2 = 2x + 3$$ 3. To isolate $x$, subtract $2x$ from both sides: $$7x - \cancel{2x} - 2 = \cancel{2x} + 3$$ $$5x - 2 = 3$$ 4. Next, add 2 to both sides to move constants to the right: $$5x - 2 + 2 = 3 + 2$$ $$5x = 5$$ 5. Finally, divide both sides by 5 to solve for $x$: $$\frac{5x}{\cancel{5}} = \frac{5}{\cancel{5}}$$ $$x = 1$$ **Answer:** $x = 1$