1. **State the problem:** Solve the linear inequality $x - 3 > 4$. 2. **Recall the rule:** To isolate $x$, add or subtract terms on both sides. When multiplying or dividing by a negative number, reverse the inequality symbol. 3. **Add 3 to both sides:** $$x - 3 + 3 > 4 + 3$$ $$x > 7$$ 4. **Interpretation:** The solution is all values of $x$ greater than 7. 5. **Graph description:** On a number line, this is represented by a filled circle at 7 and shading to the right, indicating $x > 7$. **Final answer:** $$x > 7$$