1. **State the problem:** Solve the inequality $$\frac{x + 3}{3} - \frac{x - 7}{2} \geq 3$$ and interpret the solution. 2. **Write the inequality:** $$\frac{x + 3}{3} - \frac{x - 7}{2} \geq 3$$ 3. **Find a common denominator to combine fractions:** The denominators are 3 and 2, so the common denominator is 6. 4. **Rewrite each fraction with denominator 6:** $$\frac{x + 3}{3} = \frac{2(x + 3)}{6} = \frac{2x + 6}{6}$$ $$\frac{x - 7}{2} = \frac{3(x - 7)}{6} = \frac{3x - 21}{6}$$ 5. **Substitute back into the inequality:** $$\frac{2x + 6}{6} - \frac{3x - 21}{6} \geq 3$$ 6. **Combine the fractions:** $$\frac{2x + 6 - (3x - 21)}{6} \geq 3$$ 7. **Simplify the numerator:** $$2x + 6 - 3x + 21 = -x + 27$$ So the inequality is: $$\frac{-x + 27}{6} \geq 3$$ 8. **Multiply both sides by 6 to clear the denominator:** $$\cancel{6} \times \frac{-x + 27}{\cancel{6}} \geq 3 \times 6$$ $$-x + 27 \geq 18$$ 9. **Isolate $x$:** $$-x \geq 18 - 27$$ $$-x \geq -9$$ 10. **Multiply both sides by -1 and reverse the inequality sign:** $$\cancel{-1} \times (-x) \leq \cancel{-1} \times (-9)$$ $$x \leq 9$$ **Final solution:** $$x \leq 9$$ **Note:** The graph you described shows $x \geq 3$, but the solution to the inequality is $x \leq 9$. Possibly the graph is for a different inequality or part of a compound inequality.