Prep · One-variable equations

1. 1.

   Solve 3x = 30.

   Answer. x = 10

   Divide both sides by 3: x = 303 = 10.

2. 2.

   Solve x + 11 = 15.

   Answer. x = 4

   Subtract 11 from both sides: x = 15 − 11 = 4.

3. 3.

   Solve 8x + 4 = 60.

   Answer. x = 7

   Subtract 4: 8x = 56. Divide by 8: x = 7.

4. 4.

   Solve 3x = 9.

   Answer. x = 3

   Divide both sides by 3: x = 93 = 3.

5. 5.

   Jonah has some marbles, gets 3 more, and then has 12. How many did Jonah start with?

   Answer. 9

   x + 3 = 12 → x = 9.

6. 6.

   Mei pays $1 plus $7 per game and spends $64 total. How many games?

   Answer. 9

   7x + 1 = 64 → x = 9.

7. 7.

   Malik’s tickets cost $3 each and the total is $12. How many tickets did Malik buy? Then Malik gives 1 away. How many are left?

   Answer. 3

   3x = 12 → x = 4 tickets. After giving 1 away: 3.

8. 8.

   Grace has some marbles, gets 8 more, and then has 17. How many did Grace start with?

   Answer. 9

   x + 8 = 17 → x = 9.

9. 9.

   Grace pays $4 plus $6 per game and spends $16 total. How many games?

   Answer. 2

   6x + 4 = 16 → x = 2.

10. 10.

    Nora’s tickets cost $6 each and the total is $36. How many tickets did Nora buy? Then Nora gives 1 away. How many are left?

    Answer. 5

    6x = 36 → x = 6 tickets. After giving 1 away: 5.

11. 11.

    Think

    Priya solved x + 4 = 8 by adding 4 to 8 and got 12. What is x?

    Answer. x = 4

    Undo addition with subtraction: x = 8 − 4 = 4.

12. 12.

    Think

    Owen divided 102 by 8 first on 8x + 6 = 102 and got x = 12.75. Undo addition first. What is x?

    Answer. x = 12

    Subtract 6, then divide by 8: x = 12.

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