1. **State the problems:** We have two separate problems to solve: **Problem 1:** Solve the inequality $$19 - 2x > 9$$. **Problem 2:** Solve the equation $$\frac{m}{3} = \frac{1 - m}{5}$$. 2. **Solve Problem 1:** Given: $$19 - 2x > 9$$ Step 1: Subtract 19 from both sides: $$19 - 2x - 19 > 9 - 19$$ $$-2x > -10$$ Step 2: Divide both sides by $$-2$$. Remember, dividing by a negative number reverses the inequality: $$\frac{-2x}{-2} < \frac{-10}{-2}$$ $$x < 5$$ 3. **Solve Problem 2:** Given: $$\frac{m}{3} = \frac{1 - m}{5}$$ Step 1: Cross multiply to eliminate fractions: $$5m = 3(1 - m)$$ Step 2: Distribute the 3 on the right side: $$5m = 3 - 3m$$ Step 3: Add $$3m$$ to both sides: $$5m + 3m = 3$$ $$8m = 3$$ Step 4: Divide both sides by 8: $$m = \frac{3}{8}$$ **Final answers:** - For the inequality: $$x < 5$$ - For the equation: $$m = \frac{3}{8}$$