1. **State the problem:** Solve the inequality $$3x + 7 > 43$$ and graph the solution set. 2. **Formula and rules:** To solve linear inequalities, isolate the variable on one side by performing inverse operations. Remember, when multiplying or dividing both sides by a negative number, reverse the inequality sign. 3. **Step-by-step solution:** 1. Start with the inequality: $$3x + 7 > 43$$ 2. Subtract 7 from both sides to isolate the term with $$x$$: $$3x + 7 - 7 > 43 - 7$$ $$3x > 36$$ 3. Divide both sides by 3 to solve for $$x$$: $$\frac{3x}{3} > \frac{36}{3}$$ $$x > 12$$ 4. **Interpretation:** The solution set includes all real numbers greater than 12. 5. **Graphing:** On a number line, draw an open circle at 12 (since 12 is not included) and shade all values to the right of 12. **Final answer:** $$x > 12$$