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      Solving two step linear equations

      I can see that when an additive step and a multiplicative step are required to solve an equation, the order of operations will not affect the solution.

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      Lesson 10 of 17
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      • Year 8

      Solving two step linear equations

      I can see that when an additive step and a multiplicative step are required to solve an equation, the order of operations will not affect the solution.

      Lesson details

      Key learning points

      1. When an equation is in the form Ax + B = C you can solve by first subtracting B from both sides.
      2. When an equation is in the form Ax + B = C you can solve by first dividing both sides by A.
      3. These two options give the same solution.
      4. In any particular situation one way may be more efficient than the other and it useful to think carefully about this.

      Keywords

      • Equation - An equation is used to show two expressions that are equal to each other.

      Common misconception

      That there is only one way to solve any given equation.

      In maths we will often see multiple ways to solve the same one problem. To be able to use multiple methods is a demonstration of fluency.

      Ask pupils to solve the same equation twice using two different methods. Get them to compare the methods and their efficiency. This will better prepare pupils for more complex equations.
      Teacher tip

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      An equation is used to show two expressions that are to each other.

      Correct Answer: equal, Equal

      Q2.
      Work out the value of $$13+7+(−7)$$

      $$6$$
      $$7$$
      Correct answer: $$13$$
      $$20$$

      Q3.
      Work out the value of $${20 \over 4}$$

      $$4$$
      Correct answer: $$5$$
      $$16$$
      $$20$$
      $$80$$

      Q4.
      Solve the equation $$x + 9 = 21$$

      $$x=9$$
      Correct answer: $$x=12$$
      $$x=21$$
      $$x=30$$

      Q5.
      Solve the equation $$5x = 15$$

      Correct answer: $$x=3$$
      $$x=5$$
      $$x=10$$
      $$x=75$$

      Q6.
      Solve the equation $$7x = 3$$

      $$x=−4$$
      Correct answer: $$x={3\over7}$$
      $$x={7\over3}$$
      $$x=21$$
      It can't be solved because $$7$$ is not divisible by $$3$$

      Assessment exit quiz

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      6 Questions

      Q1.
      The solution to an equation is the value which, when substituted, maintains the between the two expressions.

      Correct Answer: equality, Equality

      Q2.
      Which is the most useful additive first step to apply to both sides when solving $$7y − 3=18$$?

      $$−3$$
      Correct answer: $$+3$$
      $$−7$$
      $$−18$$

      Q3.
      Solve $$3y + 7 = 19$$

      $$y=3$$
      $$3y=12$$
      Correct answer: $$y=4$$
      $$y=12$$

      Q4.
      Which is the most useful multiplicative first step to apply to both sides when solving $$6y−12=18$$?

      $$\div 2$$
      $$\div 3$$
      Correct answer: $$\div 6$$
      $$\times 3$$
      $$\times 6$$

      Q5.
      Match each equation to its solution.

      Correct Answer:$$2x+3=4$$,$$x={1\over2}$$
      Correct Answer:$$3x+2=4$$,$$x={2\over3}$$
      Correct Answer:$$2x+4=3$$,$$x=−{1\over2}$$
      Correct Answer:$$3x+4=2$$,$$x=−{2\over3}$$
      Correct Answer:$$4x+3=2$$,$$x=−{1\over4}$$
      Correct Answer:$$4x+2=3$$,$$x={1\over4}$$

      Q6.
      $$x=$$ is the solution to the equation $${x\over8}+{1\over4}={1\over2}$$

      Correct Answer: 2, two, x=2

      Lesson appears in

      UnitMaths / Solving linear equations

      Maths

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