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MathidiaMathematics Academy
Expressions and equations
Lesson 40 of 75
Review

Solve two-step equations

Objective. Solve and check linear equations requiring two inverse steps.

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  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A two-step equation requires two inverse operations performed in the correct order to isolate the variable, usually undoing addition or subtraction before multiplication or division. For example, to solve 3x+4=19, first subtract 4 from both sides to get 3x=15, then divide both sides by 3 to get x=5. The order matters because the equation was built up by multiplying first and then adding, so solving reverses that order. Always check your answer by substituting it back into the original equation to confirm both sides match.

Worked example

Solve the two-step equation 5x − 8 = 27.

5 … 8
Illustrated card showing 5 … 8
  1. 1Add 8 to both sides to remove the constant: 5x=35.
  2. 2Divide both sides by 5: x=7.
  3. 3Check by substituting back: 5×7−8=35−8=27.
  4. 4The left side matches the right side, confirming the solution.

Answer: x = 7

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Common mistake. Pupils sometimes divide by the coefficient before dealing with the added or subtracted constant, turning 3x+4=19 into x+4=6.33 incorrectly. Always remove the constant term first.

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