L11 · Number of solutions

1. 1.

   How many solutions does 5x + 5 = 5x + 8 have?

   Answer. none

   Subtract 5x: 5 = 8, which is never true.

2. 2.

   How many solutions does 3x + 5 = 3(x) + 5 have?

   Answer. infinitely many

   Both sides are identical, so every x works.

3. 3.

   How many solutions does 4x + 1 = 21 have?

   Answer. one

   Subtract 1: 4x = 20 → x = 5, a single value.

4. 4.

   How many solutions does 6x + 2 = 6x + 5 have?

   Answer. none

   Subtract 6x: 2 = 5, which is never true.

5. 5.

   How many solutions does 4x + 1 = 4(x) + 1 have? Write a complete answer — Ava will compare with a partner.

   Answer. infinitely many

   Both sides are identical, so every x works.

6. 6.

   How many solutions does 4x + 1 = 17 have? Write a complete answer — Mei will compare with a partner.

   Answer. one

   Subtract 1: 4x = 16 → x = 4, a single value.

7. 7.

   How many solutions does 4x + 4 = 4x + 7 have? Write a complete answer — Owen will compare with a partner.

   Answer. none

   Subtract 4x: 4 = 7, which is never true.

8. 8.

   How many solutions does 2x + 4 = 2(x) + 4 have? Write a complete answer — Luis will compare with a partner.

   Answer. infinitely many

   Both sides are identical, so every x works.

9. 9.

   How many solutions does 3x + 1 = 16 have? Write a complete answer — Nora will compare with a partner.

   Answer. one

   Subtract 1: 3x = 15 → x = 5, a single value.

10. 10.

    How many solutions does 4x + 8 = 4x + 11 have? Write a complete answer — Jonah will compare with a partner.

    Answer. none

    Subtract 4x: 8 = 11, which is never true.

11. 11.

    Think

    Theo tried this problem:
    How many solutions does 6x + 4 = 6(x) + 4 have?
    Theo wrote infinitely many (check this). That is not correct. What is the right answer?

    Answer. infinitely many

    Theo’s answer infinitely many (check this) is off. Both sides are identical, so every x works.

12. 12.

    Think

    Mei tried this problem:
    How many solutions does 5x + 1 = 26 have?
    Mei wrote one (check this). That is not correct. What is the right answer?

    Answer. one

    Mei’s answer one (check this) is off. Subtract 1: 5x = 25 → x = 5, a single value.

Original extra practice. Keys are computed from the items, not guessed.