Lesson 3: Solving Equations with Variables on Both Sides — Practice Questions

1. 1. When solving an equation, which of the following resulting statements indicates that the equation has no solution?

   • A. $x = 5$
   • B. $8 = 8$
   • C. $4 = -1$
   • D. $0 = 0$

2. 2. How many solutions does the equation $8y + 6 = 8y - 3$ have? If there are no solutions, enter 'no solution'.

3. 3. Solve the equation $5(k + 2) = 5k + 12$. If there is no solution, enter 'no solution'. The solution is ___.

4. 4. Which of the following linear equations has no solution?

   • A. $4x + 9 = 4x + 9$
   • B. $4x + 9 = 5x + 9$
   • C. $4x + 9 = 4x + 1$
   • D. $4x = 12$

5. 5. What simplified, false statement results from attempting to solve the equation $-3p + 8 = 4 - 3p$? The resulting statement is ___.

6. 6. Solve the equation for the variable x: $4x + 9 = 7x - 3$. $x$ = ___

7. 7. Solve the following equation for y: $3(2y - 5) = 4y + 1$. $y$ = ___

8. 8. What is the result after simplifying both sides of the equation $2(a + 5) - 3 = 3(a - 1) + a$?

   • A. $2a + 7 = 4a - 3$
   • B. $2a + 2 = 4a - 3$
   • C. $2a + 7 = 3a - 2$
   • D. $2a + 5 = 4a - 1$

9. 9. Solve the equation for the variable z: $5(z - 3) + 2 = 2(3z + 1) - 4$. $z$ = ___

10. 10. Solve the equation for k, expressing your answer as a fraction if necessary: $8k - 10 = 5k - 2$. $k$ = ___