Equations with x on both sides, including no solution or infinitely many

Answer Key - Grade 8 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Pia draws bars for 3x + 3 = x + 11, with x pieces on both bars. What is x?

   4
2. 2.

   Two bars of equal value, labeled, not drawn to length. Ren colors the bars for 5x − 3 = x + 21, using a different crayon for each bar. What is x?

   6
3. 3.

   Tala sketches 7x − 2 = 2x + 23 as two bars on lined paper. What is x?

   5
4. 4.

   The math club warm-up is x + 7 = 3x + 3, and Ari wants to finish first. What is x?

   2
5. 5.

   Esme's quiz begins with 7x − 2 = 5x + 14. What is x?

   8
6. 6.

   Jun looks at 2x + 5 = 2x + 9 on the bonus board. How many solutions does it have?

   • No solution
   • Exactly one solution
   • Infinitely many solutions
7. 7.

   Kira compares both sides of 3x + 4 = 3x + 4. How many solutions does it have?

   • Exactly one solution
   • Infinitely many solutions
   • No solution
8. 8.

   Luz spots 4x − 3 = 4x + 2 on a puzzle card. How many solutions does it have?

   • Exactly one solution
   • No solution
   • Infinitely many solutions
9. 9.

   Noah sees x on both sides of 3x + 1 = x + 9 on a paper puzzle card. How many solutions does it have?

   • No solution
   • Infinitely many solutions
   • Exactly one solution
10. 10.

    Tala checks a friend's answers to 4x − 1 = 2x + 17 before class. Which value of x makes it true?

    • -9
    • 9
    • 8
    • 3