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.

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

   9
2. 2.

   Tala faces brackets on both bars on paper: 2(x + 3) = 4(x − 2). What is x?

   7
3. 3.

   Zee unwraps 6(x + 2) = 3(x + 9), one bracket at a time. What is x?

   5
4. 4.

   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
5. 5.

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

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

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

   4
7. 7.

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

   6
8. 8.

   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
9. 9.

   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
10. 10.

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

    • 3
    • 40
    • 10
    • 5