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Two-step equations worksheets

Twenty equations needing two steps, such as 3x + 5 = 20, in three versions with answer keys. Every answer is a whole number.

Two-step equations: ax + b = c

NameDate

Solve for x.

  1. 8x − 19 = 45, x =
  2. 9x + 7 = 34, x =
  3. 6x + 13 = 67, x =
  4. 7x − 15 = 27, x =
  5. x ÷ 5 + 4 = 15, x =
  6. x ÷ 4 + 5 = 15, x =
  7. 6x − 15 = 57, x =
  8. 6x + 5 = 47, x =
  9. 5x + 19 = 74, x =
  10. x ÷ 9 + 14 = 20, x =
  11. 2x + 10 = 22, x =
  12. 4x + 9 = 37, x =
  13. 6x + 6 = 48, x =
  14. 5x − 1 = 49, x =
  15. 4x + 20 = 60, x =
  16. x ÷ 8 + 13 = 18, x =
  17. x ÷ 6 + 9 = 19, x =
  18. 6x + 20 = 92, x =
  19. 8x − 11 = 61, x =
  20. 8x + 19 = 99, x =
Sheet AFree at teach.peabody.kids

Two-step equations: ax + b = c

NameDate

Solve for x.

  1. 3x − 16 = 2, x =
  2. 5x − 6 = 39, x =
  3. x ÷ 8 + 9 = 11, x =
  4. 6x + 11 = 23, x =
  5. 4x − 19 = 13, x =
  6. 5x + 2 = 47, x =
  7. x ÷ 2 + 19 = 31, x =
  8. 8x − 11 = 85, x =
  9. 8x + 15 = 39, x =
  10. 3x − 12 = 15, x =
  11. x ÷ 2 + 18 = 30, x =
  12. 7x + 4 = 81, x =
  13. 7x − 5 = 37, x =
  14. x ÷ 3 + 16 = 26, x =
  15. 2x + 3 = 13, x =
  16. 9x − 9 = 99, x =
  17. 8x + 3 = 91, x =
  18. x ÷ 5 + 12 = 15, x =
  19. 8x − 13 = 19, x =
  20. x ÷ 2 + 3 = 9, x =
Sheet BFree at teach.peabody.kids

Two-step equations: ax + b = c

NameDate

Solve for x.

  1. 7x + 20 = 62, x =
  2. 9x + 14 = 86, x =
  3. x ÷ 6 + 3 = 11, x =
  4. 6x − 9 = 9, x =
  5. x ÷ 5 + 10 = 19, x =
  6. 5x − 18 = 37, x =
  7. 2x − 9 = 1, x =
  8. 2x − 9 = 11, x =
  9. x ÷ 3 + 8 = 16, x =
  10. 4x − 7 = 37, x =
  11. x ÷ 8 + 20 = 29, x =
  12. 2x + 13 = 37, x =
  13. 7x − 20 = 1, x =
  14. 4x − 14 = 34, x =
  15. 8x + 16 = 112, x =
  16. x ÷ 2 + 1 = 7, x =
  17. 6x − 18 = 30, x =
  18. 6x − 12 = 48, x =
  19. 4x + 19 = 47, x =
  20. 4x + 17 = 65, x =
Sheet CFree at teach.peabody.kids

Answer key

Sheet A

  1. 8
  2. 3
  3. 9
  4. 6
  5. 55
  6. 40
  7. 12
  8. 7
  9. 11
  10. 54
  11. 6
  12. 7
  13. 7
  14. 10
  15. 10
  16. 40
  17. 60
  18. 12
  19. 9
  20. 10

Sheet B

  1. 6
  2. 9
  3. 16
  4. 2
  5. 8
  6. 9
  7. 24
  8. 12
  9. 3
  10. 9
  11. 24
  12. 11
  13. 6
  14. 30
  15. 5
  16. 12
  17. 11
  18. 15
  19. 4
  20. 12

Sheet C

  1. 6
  2. 8
  3. 48
  4. 3
  5. 45
  6. 11
  7. 5
  8. 10
  9. 24
  10. 11
  11. 72
  12. 12
  13. 3
  14. 12
  15. 12
  16. 12
  17. 8
  18. 10
  19. 7
  20. 12
Answer keyFree at teach.peabody.kids

Two-step equations: 20 problems a sheet, 3 versions that do not repeat each other where the numbers allow.

How to use it

  1. Look at the sheet: it is a real, printable sheet. Switch between Sheet A, B and C, or press New numbers (N) for a fresh set.
  2. Change how many problems, how many versions, and whether the key prints. Settings stay in this browser; Share copies a link that rebuilds the same sheets.
  3. Press Print sheet A and key, or Print all. The answer key prints on its own page, so you can keep it back.

Ideas for class

  • Ask students to write each step on its own line, with the operation in the margin, so the order of the steps is visible.
  • Practice the reverse: give a solution and have students build an equation that has it.
  • Insist on a check by substitution every time. It is the quickest route to confidence with algebra.

Related

Questions

Can the solution be negative?

Not on this sheet. The seventh-grade level with negative numbers is a separate choice in the maker, under Two-step equations with negative numbers.

What about equations with parentheses or variables on both sides?

Both are in the maker as separate levels: a(x + b) = c, and variables on both sides for eighth grade. Each solution is a whole number there too.

Are the answer keys checked?

Each answer is worked out by the code that wrote the problem, and our tests recompute every answer a second way and compare. Please still look over the key before you grade a class set.

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What this worksheet covers

A two-step equation has a variable that is multiplied or divided and then has a number added or subtracted. Solving it means undoing the two operations in reverse order. This sheet has three forms: ax + b = c, ax − b = c, and x ÷ a + b = c. The numbers are chosen so that the solution is always a positive whole number, and the right-hand side is always a positive whole number too.

Who it is for

Seventh grade. Common Core 7.EE.B.4a asks students to solve equations of the form px + q = r, and it follows one-step equations. Students should be able to explain why they subtract before they divide.

Solving equations that take two steps · grade 7

A worked example

3x + 5 = 20. Subtract 5 from both sides: 3x = 15. Then divide both sides by 3: x = 5. Check: 3 × 5 + 5 = 20. The order matters: if we divided by 3 first, we would have to divide the 5 as well.

Mistakes to watch for

  • Dividing before subtracting, so 3x + 5 = 20 becomes x + 5 = 20/3. Both steps are correct, but the order creates fractions.
  • Forgetting to apply an operation to both sides. Use a balance picture or a line down the equals sign.

Make it your own

This sheet is one setting of the math worksheet generator. Open it there to change the skill, the range of numbers or the heading, or to mix several skills on one sheet.