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Lesson 15 of 17

Solving complex linear equations involving brackets

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

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Lesson 15 of 17
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Solving complex linear equations involving brackets

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

Lesson details

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.

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 $$3$$.
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.
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: $$2(7x + 3 + 4x+1)$$
$$7x+3=4x+1$$

Assessment exit quiz

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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

Lesson appears in

UnitMaths / Solving linear equations

Maths

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