1. **Problem a:** Xavier thinks of a number. He multiplies it by 2 then adds 8. The answer is 20. 2. **Write the equation:** Let the number be $x$. The equation is: $$2x + 8 = 20$$ 3. **Solve the equation:** - Subtract 8 from both sides: $$2x = 20 - 8$$ $$2x = 12$$ - Divide both sides by 2: $$x = \frac{12}{2}$$ $$x = 6$$ 4. **Answer:** Xavier thought of the number 6. 1. **Problem b:** Sasha thinks of a number. She divides it by 4 then subtracts 3. The answer is 2. 2. **Write the equation:** Let the number be $y$. The equation is: $$\frac{y}{4} - 3 = 2$$ 3. **Solve the equation:** - Add 3 to both sides: $$\frac{y}{4} = 2 + 3$$ $$\frac{y}{4} = 5$$ - Multiply both sides by 4: $$y = 5 \times 4$$ $$y = 20$$ 4. **Answer:** Sasha thought of the number 20. 1. **Problem c:** Harsha thinks of a number. She multiplies it by 4 then subtracts 6. The answer is the same as 2 times the number plus 12. 2. **Write the equation:** Let the number be $z$. The equation is: $$4z - 6 = 2z + 12$$ 3. **Solve the equation:** - Subtract $2z$ from both sides: $$4z - 2z - 6 = 12$$ $$2z - 6 = 12$$ - Add 6 to both sides: $$2z = 12 + 6$$ $$2z = 18$$ - Divide both sides by 2: $$z = \frac{18}{2}$$ $$z = 9$$ 4. **Answer:** Harsha thought of the number 9.