1. **State the problem:** We need to solve the equation $2x + 3 = 7$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse operations. 3. **Step 1:** Subtract 3 from both sides: $$2x + 3 - 3 = 7 - 3$$ which simplifies to $$2x = 4$$ 4. **Step 2:** Divide both sides by 2 to solve for $x$: $$\frac{\cancel{2}x}{\cancel{2}} = \frac{4}{2}$$ which simplifies to $$x = 2$$ 5. **Answer:** The solution to the equation is $x = 2$. This means when $x$ is 2, the original equation holds true.