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.

   Noah joins thirds and sixths in (8/3)x + 2 = x/6 + 12. What is x?

   4
3. 3.

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

   5
4. 4.

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

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

   Jun has a bracket on the right in 5x + 3 = 5(x + 1). How many solutions does it have?

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

   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
7. 7.

   Noah wants 5(x + 2) − 4 = 5x + c to be true for every x. What number must c be?

   6
8. 8.

   Ren has read 28 pages and reads 2 a day. A friend has read 10 pages and reads 5 a day. After how many days have both read the same number of pages?

   6
9. 9.

   Tala starts 5 miles from the park and bikes away at 11 mph. A friend starts 21 miles out and bikes away at 7 mph. After how many hours are both equally far out?

   4
10. 10.

    Ari checks four guesses for 8x − 5 = 6x + 9. Which value of x makes it true?

    • 2
    • 14
    • 7
    • 1