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Solving complex linear equations

I can solve complex linear equations, including those involving reciprocals.

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Lesson 12 of 17

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Year 8

Solving complex linear equations

I can solve complex linear equations, including those involving reciprocals.

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Lesson details

Key learning points

Any linear equation written in the form Ax + B = C can be solved.
Equations involving division by a constant can be manipulated to reach the form Ax + B = C.
Equations involving division by a variable can be manipulated to reach the form Ax + B = C.

Keywords

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

Common misconception

Pupils often "multiply through by $$5$$" and turn $${{2x+1}\over5}={10}$$ into $${{10x+5}}={50}$$

Use equivalent fractions as opposed to multiplying through. In one simple step $${{2x+1}\over5}={10}$$ becomes $${{2x+1}\over5}={50\over5}$$

The key is for pupils to be able to fluently use their fractions skills and knowledge when manipulating algebra. Use a numerical fractions starter to ensure they recall key skills like multiplying a fraction by an integer, and by another fraction.

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).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
$$1\over7$$ is the of $$7$$

fraction

division

Correct answer: reciprocal

divisor

multiplier

Q2.
Solve $$6x+9=27$$

Correct answer: $$x=3$$

$$x=6$$

$$x=9$$

$$x=18$$

Q3.
Solve $${x\over3}=15$$

Correct answer: $$x=45$$

$$x=18$$

$$x=5$$

$$x={1\over5}$$

Q4.
Calculate $${2\over3}\times{4\over5}$$

$$6\over15$$

$$6\over20$$

Correct answer: $$8\over15$$

$$10\over12$$

$$12\over10$$

Q5.
Which of these expressions are equivalent to $${{x+1}\over3}\times{2\over3}$$ ?

$${2x+1}\over9$$

Correct answer: $${2{(x+1)}\over9}$$

$${2{(x+1)}\over3}$$

$${2x+2}\over3$$

Correct answer: $${2x+2}\over9$$

Q6.
Expand and simplify $$8({{x}\over8})$$

$$8$$

Correct answer: $$x$$

$$8x$$

$${{8x}\over8}$$

$$x=8$$

Assessment exit quiz

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6 Questions

Q1.
$${{56}\over{y}}=7$$ is an example of a equation.

variable

Correct answer: rational

irrational

special

Q2.
The solution to $${{6x−2}\over{4}}=7$$ is $$x=$$

Correct Answer: 5, five

Q3.
Solve $${{2x}\over{3}}+1=11$$

Correct answer: $$x=15$$

$$x=16$$

$$x=17$$

$$x=18$$

Q4.
Which is the most efficient first step when solving the equation $${{x+7}\over{9}}={{x-1}\over{3}}$$ ?

Subtract $$7$$ from both sides.

Add $$1$$ to both sides.

Correct answer: Multiply both sides by $$9$$

Multiply both sides by $$3$$

Multiply both sides by $$27$$

Q5.
Solve $${{x+7}\over{9}}={{x−1}\over{3}}$$. The solution is $$x=$$

Correct Answer: 5, five

Q6.
Solve $${{32}\over{3x}}=8$$

$$x={3\over4}$$

$$x=3$$

$$x=4$$

Correct answer: $$x={4\over3}$$

Lesson appears in

UnitMaths / Solving linear equations

Maths

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Solving complex linear equations

Solving complex linear equations

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.$$1\over7$$ is the of $$7$$

Q2.Solve $$6x+9=27$$

Q3.Solve $${x\over3}=15$$

Q4.Calculate $${2\over3}\times{4\over5}$$

Q5.Which of these expressions are equivalent to $${{x+1}\over3}\times{2\over3}$$ ?

Q6.Expand and simplify $$8({{x}\over8})$$

Assessment exit quiz

6 Questions

Q1.$${{56}\over{y}}=7$$ is an example of a equation.

Q2.The solution to $${{6x−2}\over{4}}=7$$ is $$x=$$

Q3.Solve $${{2x}\over{3}}+1=11$$

Q4.Which is the most efficient first step when solving the equation $${{x+7}\over{9}}={{x-1}\over{3}}$$ ?

Q5.Solve $${{x+7}\over{9}}={{x−1}\over{3}}$$. The solution is $$x=$$

Q6.Solve $${{32}\over{3x}}=8$$

Lesson appears in

UnitMaths / Solving linear equations

Maths

Q1.
$$1\over7$$ is the of $$7$$

Q2.
Solve $$6x+9=27$$

Q3.
Solve $${x\over3}=15$$

Q4.
Calculate $${2\over3}\times{4\over5}$$

Q5.
Which of these expressions are equivalent to $${{x+1}\over3}\times{2\over3}$$ ?

Q6.
Expand and simplify $$8({{x}\over8})$$

Q1.
$${{56}\over{y}}=7$$ is an example of a equation.

Q2.
The solution to $${{6x−2}\over{4}}=7$$ is $$x=$$

Q3.
Solve $${{2x}\over{3}}+1=11$$

Q4.
Which is the most efficient first step when solving the equation $${{x+7}\over{9}}={{x-1}\over{3}}$$ ?

Q5.
Solve $${{x+7}\over{9}}={{x−1}\over{3}}$$. The solution is $$x=$$

Q6.
Solve $${{32}\over{3x}}=8$$