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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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Year 8

Solving complex linear equations involving brackets

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

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Lesson slides

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Lesson details

Key learning points

Brackets where an expression is multiplied by a term can be expanded.
Like terms can then be collected so the equation is in a form that can be solved.
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

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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).

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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?

$$(7x+3)+(4x+1)$$

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 $$x$$?

$$9x+14=154$$

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 .

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

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UnitMaths / Solving linear equations

Maths

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Solving complex linear equations involving brackets

Solving complex linear equations involving brackets

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

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

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

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

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

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

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

Assessment exit quiz

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 .

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

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

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

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

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

Lesson appears in

UnitMaths / Solving linear equations

Maths

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

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

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

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

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

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

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 .

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

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

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

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

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