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Two-step equations: 7th grade math

Linear expressions with rational coefficients; two-step equations (px + q = r) and inequalities. A free 7th grade lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: linear expressions with rational coefficients; two-step equations (px + q = r) and inequalities.

Teach (10 min)

  • Undo in reverse order. 3x + 5 = 20: subtract 5 to get 3x = 15, then divide by 3 to get x = 5.
  • A tape diagram helps with a story: a $135 bill is $45 plus some $30 hours. Take off $45, and $90 is x pieces of $30, so x = 3.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/algebra.twoStep?lesson=7-algebra-two-step&at=7

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. Solve 2x + 2 = 12. x = ?
  • 2. Solve 3x + 5 = 20. x = ?
  • 3. Solve 4x + 3 = 11. x = ?

Question set

10 questions that read in words, easiest first. Questions that need a picture are on the printable sheet below.

  1. Solve 2x + 2 = 12. x = ?
  2. Solve 3x + 5 = 20. x = ?
  3. Solve 4x + 3 = 11. x = ?
  4. Solve 4x + 1 = 25. x = ?
  5. Solve 3x + 1 = 4. x = ?
  6. Solve 3x + 8 = 35. x = ?
  7. Solve 2x + 8 = 12. x = ?
  8. Solve 4x + 1 = 5. x = ?
  9. Solve 3x + 8 = 14. x = ?
  10. A student has $60 saved and adds $2 every week. After how many weeks will the student have $70?
Answers
  1. 5
  2. 5
  3. 2
  4. 6
  5. 1
  6. 9
  7. 2
  8. 1
  9. 2
  10. 5 weeks

Printable sheet

Name: ____________________   Date: ____________

Two-step equations (7th grade)

  1. Solve 2x + 2 = 18. x = ?
  2. Solve 4x + 2 = 6. x = ?
  3. Solve 5x + 1 = 41. x = ?
  4. Solve 5x + 9 = 19. x = ?
  5. A gift card has $46 on it. Each sandwich costs $4. After some sandwiches are bought, $22 is left. How many sandwiches were bought?
  6. A student owes $27 and pays back $3 every week. After how many weeks will $12 still be owed?
  7. Solve 5x − 9 = 36. x = ?
  8. Solve 7x − 2 = 61. x = ?
  9. Solve 3x + 9 = 3. x = ?
  10. A photographer charges $11 to set up and $40 for each hour of shooting. The total is $331. How many hours of shooting was it?
  11. A tank holds 15 liters of water. A hose adds 9 liters every minute. How many minutes until the tank holds 69 liters?
  12. Solve x2 − 10 = −15. x = ?
Key
  1. 8
  2. 1
  3. 8
  4. 2
  5. 6 sandwiches
  6. 5 weeks
  7. 9
  8. 9
  9. −2
  10. 8 hours
  11. 6 minutes
  12. −10

Written by Peabody from its own skill pages. Free, no ads, no sign-in. Children can practise this on Peabody. More from teachers: teacher-shared resources.