1. **State the problem:** Solve the linear equation $2x - 1 = 3$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Addition/subtraction and multiplication/division are used to simplify the equation. 3. **Step 1:** Add 1 to both sides to eliminate the $-1$ on the left: $$2x - 1 + 1 = 3 + 1$$ $$2x = 4$$ 4. **Step 2:** Divide both sides by 2 to solve for $x$: $$\frac{2x}{2} = \frac{4}{2}$$ $$x = 2$$ 5. **Answer:** The solution to the equation $2x - 1 = 3$ is $x = 2$. This means when $x$ is 2, the original equation holds true.