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.

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

   5
2. 2.

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

   • Infinitely many solutions
   • No solution
   • Exactly one solution
3. 3.

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

   • Infinitely many solutions
   • Exactly one solution
   • No solution
4. 4.

   Milo needs the sides of 2(x − 3) + 10 = 2x + c to match for every x. What number must c be?

   4
5. 5.

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

   6
6. 6.

   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
7. 7.

   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
8. 8.

   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
9. 9.

   Zee tests four values for 6(x − 4) = 2(x + 8). Which value of x makes it true?

   • 40
   • 10
   • 3
   • 5
10. 10.

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

    • 7
    • 1
    • 14
    • 2