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

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Milo's decimal puzzle reads 3.5x + 3 = 1.5x + 13. What is x?

   5
2. 2.

   Pia's card has fractions and a minus: (7/3)x − 2 = (2/3)x + 13. What is x?

   9
3. 3.

   Ren spreads on both sides of 6(x − 2) = 2(x + 4). What is x?

   5
4. 4.

   Ari spreads and joins in 3(x + 2) + x = 4x + 6. How many solutions does it have?

   • Exactly one solution
   • No solution
   • Infinitely many solutions
5. 5.

   Bo takes a bracket away in -2(x + 1) + 4x = 2x + 5. How many solutions does it have?

   • Exactly one solution
   • Infinitely many solutions
   • No solution
6. 6.

   Esme spreads and combines in 2(x + 5) − 4 = 2x + 6. How many solutions does it have?

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

   Kira sees x on both sides of 4(x + 2) = 2x + 10. How many solutions does it have?

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

   Luz's paper card has a hidden number: 4(x + 2) + 1 = 4x + c. For which number c does it have infinitely many solutions?

   9
9. 9.

   Pia's sprout is 5 cm tall and grows 4 cm a week. The class sprout is 11 cm tall and grows 1 cm a week. After how many weeks are they the same height?

   2
10. 10.

    Bo has four possible answers on paper for 9x + 3 = 6x + 18. Which value of x makes it true?

    • 5
    • 7
    • 15
    • 1