L21 · One-variable equations

1. 1.

   Solve 4x = 40.

   Answer. x = 10

   Divide both sides by 4: x = 404 = 10.

2. 2.

   Solve x + 11 = 17.

   Answer. x = 6

   Subtract 11 from both sides: x = 17 − 11 = 6.

3. 3.

   Solve 3x + 2 = 38.

   Answer. x = 12

   Subtract 2: 3x = 36. Divide by 3: x = 12.

4. 4.

   Solve 7x = 28.

   Answer. x = 4

   Divide both sides by 7: x = 287 = 4.

5. 5.

   Mei has some marbles, gets 17 more, and then has 19. How many did Mei start with?

   Answer. 2

   x + 17 = 19 → x = 2.

6. 6.

   Owen pays $10 plus $5 per game and spends $30 total. How many games?

   Answer. 4

   5x + 10 = 30 → x = 4.

7. 7.

   Grace’s tickets cost $6 each and the total is $78. How many tickets did Grace buy? Then Grace gives 1 away. How many are left?

   Answer. 12

   6x = 78 → x = 13 tickets. After giving 1 away: 12.

8. 8.

   Luis has some marbles, gets 9 more, and then has 20. How many did Luis start with?

   Answer. 11

   x + 9 = 20 → x = 11.

9. 9.

   Luis pays $1 plus $3 per game and spends $22 total. How many games?

   Answer. 7

   3x + 1 = 22 → x = 7.

10. 10.

    Elena’s tickets cost $8 each and the total is $48. How many tickets did Elena buy? Then Elena gives 1 away. How many are left?

    Answer. 5

    8x = 48 → x = 6 tickets. After giving 1 away: 5.

11. 11.

    Think

    Grace solved x + 5 = 12 by adding 5 to 12 and got 17. What is x?

    Answer. x = 7

    Undo addition with subtraction: x = 12 − 5 = 7.

12. 12.

    Think

    Luis divided 37 by 5 first on 5x + 7 = 37 and got x = 7.4. Undo addition first. What is x?

    Answer. x = 6

    Subtract 7, then divide by 5: x = 6.

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