1. **State the problem:** Solve the compound inequality $$v - 20 \geq -5 \text{ or } v - 15 < -3$$ and graph the solution on a number line. 2. **Solve each inequality separately:** - For $$v - 20 \geq -5$$, add 20 to both sides: $$v - 20 + 20 \geq -5 + 20$$ $$v \geq 15$$ - For $$v - 15 < -3$$, add 15 to both sides: $$v - 15 + 15 < -3 + 15$$ $$v < 12$$ 3. **Combine the solutions:** The solution is $$v \geq 15$$ or $$v < 12$$. 4. **Interpret the solution:** This means all values less than 12, and all values greater than or equal to 15 satisfy the inequality. 5. **Graph the solution:** - Draw a number line from 11 to 19. - For $$v < 12$$, plot an open circle at 12 and shade to the left. - For $$v \geq 15$$, plot a closed circle at 15 and shade to the right. - The region between 12 and 15 is not included. **Final answer:** $$v < 12 \text{ or } v \geq 15$$