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Two-step equations

Use two inverse operations to solve for x.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Solution values

Sets the possible integer solution x for both equation forms.

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mathsprig-1
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2f165761
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1 page
Two-step equationsTwo-step equations. Practice. Solve for x: 3(x − 7) = 3. Solve for x: −5(x + 2) = −40. Solve for x: −3x + 5 = 26. Solve for x: −7x + 10 = −18. Solve for x: −6(x − 4) = 84. Solve for x: 3(x − 4) = −21. Solve for x: 9x + 10 = −26. Solve for x: 5(x + 8) = 15. Solve for x: 9(x + 3) = 90. Solve for x: 8x + 4 = 12. Solve for x: 8(x − 5) = 32. Solve for x: 3x + 5 = −22.Name __________________________Date _______________Two-step equationsSolve for x and show your steps.Worked exampleSolve 2(x + 3) = 14. → x = 4Divide both sides by 2: x + 3 = 7.1.Solve for x: 3(x − 7) = 3.2.Solve for x: −5(x + 2) = −40.3.Solve for x: −3x + 5 = 26.4.Solve for x: −7x + 10 = −18.5.Solve for x: −6(x − 4) = 84.6.Solve for x: 3(x − 4) = −21.7.Solve for x: 9x + 10 = −26.8.Solve for x: 5(x + 8) = 15.9.Solve for x: 9(x + 3) = 90.10.Solve for x: 8x + 4 = 12.11.Solve for x: 8(x − 5) = 32.12.Solve for x: 3x + 5 = −22.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 2f165761
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Practice + answer key · 2 pages

Algebra

What you’ll practice

Solve ax + b = c and a(x + b) = c.

Work backward through the operations around x. For 2(x + 3) = 14, divide both sides by 2 before subtracting 3.

How this skill works

For ax + b = c, subtract b on both sides, then divide by a.

For a(x + b) = c, divide both sides by a, then subtract b. The nonzero coefficient makes both operations reversible.

Worked example

Solve 2(x + 3) = 14.
  1. Divide both sides by 2: x + 3 = 7.
  2. Subtract 3 from both sides: x = 4.
  3. Check: 2(4 + 3) = 14.

Answer: x = 4

Teaching notes

  • Keep parentheses visible until their outside operation is removed.
Practice questions
  1. Solve for x: 3(x − 7) = 3.
  2. Solve for x: −5(x + 2) = −40.
  3. Solve for x: −3x + 5 = 26.
  4. Solve for x: −7x + 10 = −18.
  5. Solve for x: −6(x − 4) = 84.
  6. Solve for x: 3(x − 4) = −21.
  7. Solve for x: 9x + 10 = −26.
  8. Solve for x: 5(x + 8) = 15.
  9. Solve for x: 9(x + 3) = 90.
  10. Solve for x: 8x + 4 = 12.
  11. Solve for x: 8(x − 5) = 32.
  12. Solve for x: 3x + 5 = −22.
Answers and steps
  1. x = 8
    1. Divide both sides by 3: x − 7 = 1.
    2. Subtract −7 from both sides: x = 8.
    3. Substituting x = 8 gives 3 = 3.
  2. x = 6
    1. Divide both sides by −5: x + 2 = 8.
    2. Subtract 2 from both sides: x = 6.
    3. Substituting x = 6 gives −40 = −40.
  3. x = −7
    1. Subtract 5 from both sides: −3x = 21.
    2. Divide both sides by −3: x = −7.
    3. Substituting x = −7 gives 26 = 26.
  4. x = 4
    1. Subtract 10 from both sides: −7x = −28.
    2. Divide both sides by −7: x = 4.
    3. Substituting x = 4 gives −18 = −18.
  5. x = −10
    1. Divide both sides by −6: x − 4 = −14.
    2. Subtract −4 from both sides: x = −10.
    3. Substituting x = −10 gives 84 = 84.
  6. x = −3
    1. Divide both sides by 3: x − 4 = −7.
    2. Subtract −4 from both sides: x = −3.
    3. Substituting x = −3 gives −21 = −21.
  7. x = −4
    1. Subtract 10 from both sides: 9x = −36.
    2. Divide both sides by 9: x = −4.
    3. Substituting x = −4 gives −26 = −26.
  8. x = −5
    1. Divide both sides by 5: x + 8 = 3.
    2. Subtract 8 from both sides: x = −5.
    3. Substituting x = −5 gives 15 = 15.
  9. x = 7
    1. Divide both sides by 9: x + 3 = 10.
    2. Subtract 3 from both sides: x = 7.
    3. Substituting x = 7 gives 90 = 90.
  10. x = 1
    1. Subtract 4 from both sides: 8x = 8.
    2. Divide both sides by 8: x = 1.
    3. Substituting x = 1 gives 12 = 12.
  11. x = 9
    1. Divide both sides by 8: x − 5 = 4.
    2. Subtract −5 from both sides: x = 9.
    3. Substituting x = 9 gives 32 = 32.
  12. x = −9
    1. Subtract 5 from both sides: 3x = −27.
    2. Divide both sides by 3: x = −9.
    3. Substituting x = −9 gives −22 = −22.