Field Notesgrade 7 math
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Solution key: Undo twice, in the right order

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Camp · Undo twice, in the right order

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1 of 10 · two-step-c01

Solve 2x + 6 = 20. x = ?

  1. Two times x, plus 6, equals 20.
  2. Undo the plus 6 first by subtracting 6 from both sides: 20 minus 6 is 14, so 2x = 14.
  3. Then divide both sides by 2, because two groups make 14.
  4. 14 divided by 2 is 7.
  1. So x is 7.
  2. Check: 2×7+6=20.

Answer: 7

2 of 10 · two-step-c02

Solve 5x − 4 = 21. x = ?

  1. Five groups of x had 4 taken away, and 21 is left.
  2. Undo the minus 4 first by adding 4 to both sides.
  3. 21 plus 4 is 25, so 5x = 25.
  4. Divide both sides by 5: 25 divided by 5 is 5.
  1. So x is 5.
  2. Check: 5×5−4=21.

Answer: 5

3 of 10 · two-step-c03

Solve x/3 + 2 = 8. x = ?

  1. x was divided by 3, and then 2 was added to make 8.
  2. Undo the plus 2 first: 8 minus 2 is 6, so x/3 = 6.
  3. x divided by 3 equals 6 means x is 3 groups of 6.
  4. 3 times 6 is 18.
  1. So x is 18.
  2. Check: 18÷3+2=8.

Answer: 18

4 of 10 · two-step-c04

Solve 4x + 9 = 9. x = ?

  1. Four groups of x, plus 9, equals 9.
  2. The plus 9 already matches the whole right side, so subtract 9 from both sides.
  3. 9 minus 9 is 0, so 4x = 0.
  4. The only number that stays 0 when you multiply it by 4 is 0.
  1. So x is 0.
  2. Check: 4×0+9=9.

Answer: 0

5 of 10 · two-step-c05

Solve 3x − 7 = 8. x = ?

  1. Three groups of x had 7 taken away, and 8 is left.
  2. Put the 7 back by adding 7 to both sides: 8 plus 7 is 15, so 3x = 15.
  3. Divide both sides by 3 to get one group.
  4. 15 divided by 3 is 5.
  1. So x is 5.
  2. Check: 3×5−7=8.

Answer: 5

6 of 10 · two-step-c06

Solve 7 + 2x = 19. x = ?

  1. A 7 sits next to 2 groups of x, and together they make 19.
  2. Subtract 7 from both sides to leave 2x on its own.
  3. 19 minus 7 is 12, so 2x = 12.
  4. Divide both sides by 2: 12 divided by 2 is 6.
  1. So x is 6.
  2. Check: 7+2×6=19.

Answer: 6

7 of 10 · two-step-c07

Does x = 4 make 3x − 5 = 7 true? yes or no

  1. Put 4 in for x and see if both sides match.
  2. 3 times 4 is 12.
  3. Then 12 minus 5 is 7.
  1. The equation asked for 7, and the left side is 7.
  2. Check: Putting in 4 for x gives 7 = 7, so it works.

Answer: yes

8 of 10 · two-step-c08

Does x = 2 make 5x + 1 = 12 true? yes or no

  1. Put 2 in for x and work out the left side.
  2. 5 times 2 is 10.
  3. Then 10 plus 1 is 11.
  1. The equation says the left side should be 12, but 11 is not 12.
  2. Check: 11 is not 12, so x = 2 does not work.

Answer: no

9 of 10 · two-step-c09

Solve 6x + 2 = 32. x = ?

  1. Six groups of x, plus 2, equals 32.
  2. Subtract the extra 2 from both sides first.
  3. 32 minus 2 is 30, so 6x = 30.
  4. Divide both sides by 6: 30 divided by 6 is 5.
  1. So x is 5.
  2. Check: 6×5+2=32.

Answer: 5

10 of 10 · two-step-c10

Solve x/4 − 3 = 2. x = ?

  1. x was split into 4 equal parts, and then 3 was subtracted to leave 2.
  2. Add 3 back to both sides first: 2 plus 3 is 5, so x/4 = 5.
  3. One fourth of x is 5, so x is 4 times that piece.
  4. 4 times 5 is 20.
  1. So x is 20.
  2. Check: 20÷4−3=2.

Answer: 20