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.

   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
2. 2.

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

   5
3. 3.

   Zee finds 4x + 5 = x + 14 on a puzzle card and cheers. What is x?

   3
4. 4.

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

   2
5. 5.

   Bo copies 6x + 1 = 3x + 13 onto paper from the board. What is x?

   4
6. 6.

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

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

   Milo meets 6 + 2x = 2x + 6 in a book. How many solutions does it have?

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

   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
9. 9.

   Ren has four possible answers for 8x + 5 = 6x + 19. Which value of x makes it true?

   • 14
   • 12
   • 7
   • 1
10. 10.

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

    • 3
    • -9
    • 9
    • 8