1. **State the problem:** Solve the linear equation $7x - 4 = 24$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Add or subtract terms to move constants to one side, then divide to solve for $x$. 3. **Step 1:** Add 4 to both sides to cancel the $-4$ on the left: $$7x - 4 + 4 = 24 + 4$$ $$7x = 28$$ 4. **Step 2:** Divide both sides by 7 to isolate $x$: $$\frac{\cancel{7}x}{\cancel{7}} = \frac{28}{7}$$ $$x = 4$$ 5. **Final answer:** $x = 4$. This means the value of $x$ that satisfies the equation $7x - 4 = 24$ is 4.