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      Solving complex linear equations involving brackets

      Lesson details

      Learning outcome

      I can solve equations involving brackets where simplification is necessary first.

      Key learning points

      1. Brackets where an expression is multiplied by a term can be expanded.
      2. Like terms can then be collected so the equation is in a form that can be solved.
      3. Multiple identical expressions can be collected together to simplify an equation.

      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.

      Teacher tip

      Ask pupils to solve $$3(y-7)+12(y-7)=30$$ three different ways. Firstly by expanding the brackets, secondly by simplifying the identical expressions, and thirdly by dividing through by the common factor $$3$$.

      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

      6 Questions

      Q1.
      The command word to turn $$-2(5-3y)$$ into $$6y-10$$ is .

      Correct answer: 'expand'
      'solve'
      'simplify'
      'substitute'

      Q2.
      The command words to turn $$5(x+7)-3(x+2)$$ into $$2x+29$$ are .

      'expand and solve'
      Correct answer: 'expand and simplify'
      'substitute and simplify'
      'substitute and solve'

      Q3.
      Simplify $$4x+9+x-11$$

      $$4x^2-2$$
      $$4x-2$$
      $$5x+2$$
      Correct answer: $$5x-2$$
      $$5x-20$$

      Q4.
      Expand and simplify $$8(x-3)+3(5x+7)$$.

      $$8x-3+15x+7=23x+4$$
      $$8x+24+15x+21=23x+45$$
      $$8x-24-15x+21=-7x-3$$
      Correct answer: $$8x-24+15x+21=23x-3$$
      $$8x-24+15x+21=23x+3$$

      Q5.
      Which of these expressions can be simplified before the brackets are expanded?

      Correct answer: $$3(x-7)+2(x-7)$$
      $$3(x-7)+7(x-3)$$
      Correct answer: $$3(2x+5)+2(2x+5)$$
      $$3(2d+5)+2(2e+5)$$
      Correct answer: $$3(5-x)+2(5-x)$$

      Q6.
      Which of the below are expressions for the perimeter of this rectangle?

      An image in a quiz
      $$(7x+3)+(4x+1)$$
      Correct answer: $$2(7x+3)+2(4x+1)$$
      Correct answer: $$2(7x + 3 + 4x+1)$$
      $$7x+3=4x+1$$

      6 Questions

      Q1.
      You can expand brackets in the expression $$2(y+9)+2(3y-7)$$ to get the expression $$2y+18+6y-14$$. You now have like terms that can be .

      evaluated
      substracted
      Correct answer: simplified
      solved

      Q2.
      The perimeter of this rectangle is $$154$$ units. Which equation can be used to find $$x$$?

      An image in a quiz
      $$9x+14=154$$
      Correct answer: $$2(4x+15) + 2(5x-1)=154$$
      $$4x+15=5x-1=154$$
      $$2(4x+15) + 2(5x-1)$$

      Q3.
      The perimeter of this rectangle is $$154$$ units. The value of $$x$$ is .

      An image in a quiz
      Correct Answer: 7, 7 units, seven, seven units

      Q4.
      Which of these are accurate first steps when solving $$4(3x-1)-2(x+2)=72$$ ?

      $$12x-1-2x+2=72$$
      $$12x-4-2x+4=72$$
      Correct answer: $$12x-4-2x-4=72$$
      $$2(3x-1)-(x+2)=72$$
      Correct answer: $$2(3x-1)-(x+2)=36$$

      Q5.
      The solution to $$4(3x-1)-2(x+2)=72$$ is $$x=$$ .

      Correct Answer: 8, eight, x=8

      Q6.
      The solution to $$8(3x-6)-5(3x-6)=9$$ is $$x=$$ .

      Correct Answer: 3, three, x=3

      To help you plan your 8 maths lesson on: Solving complex linear equations involving brackets, download all teaching resources for free and adapt to suit your pupils' needs...