Lesson 4: Analyzing Number of Solutions (One, None, Infinite) — 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. Which of the following equations has infinitely many solutions?

   • A. 5x + 10 = 5(x + 2)
   • B. 5x + 10 = 5(x + 3)
   • C. 5x + 10 = x + 2
   • D. 5x = 10

7. 7. Find the value of $c$ that makes the equation $7x + 15 - 2x = 5x + c$ an identity. The value is ___.

8. 8. For what value of $k$ does the equation $3(2x - 1) = 6x - k$ have infinitely many solutions? The value of $k$ is ___.

9. 9. While solving an equation, you simplify it and arrive at the statement $-4 = -4$. What can you conclude about the original equation?

   • A. The equation has no solution.
   • B. The equation has infinitely many solutions.
   • C. The only solution is $x = -4$.
   • D. The only solution is $x = 0$.

10. 10. Fill in the blank with a number to create an equation with infinitely many solutions: $4(x + 5) = 4x + \_\_\_$.