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Year 8

Rearranging to solve linear equations

I can recognise that equations with unknowns on both sides of the equation can be manipulated so that the unknowns are on one side and then solve this equation.

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New
New
Year 8

Rearranging to solve linear equations

I can recognise that equations with unknowns on both sides of the equation can be manipulated so that the unknowns are on one side and then solve this equation.

Download all resources
Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Any linear equation written in the form Ax + B = C can be solved.
  2. Like terms can be collected onto one side of an equation in order to write it in the form Ax + B = C.
  3. An equation that had unknowns on both sides can then be solved.

Keywords

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

Common misconception

To subtract from both the variable and numerical terms when subtracting from both sides.

To subtract $$2$$ from $$5x+3$$ leaves $$5x+1$$, not $$3x+1$$. Use visual representations like balance scales and bar models to show this.


To help you plan your year 8 maths lesson on: Rearranging to solve linear equations, download all teaching resources for free and adapt to suit your pupils' needs...

If you have algebra tiles in your classroom use them to set up simple equations which you can then use to get pupils to "Take two ones from both groups" or "Take two $$x$$ from both groups". Get them to physically see that they are different.
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.
In order to maintain in an equation, any manipulation must be applied to both sides of the equation.

Correct answer: equality
positivity
solutions
variables

Q2.
What must be added to both sides of the equation to turn $$x=7$$ into $$x+3=10$$?

Correct answer: $$3$$
$$3x$$
$$7$$
$$10$$

Q3.
What must be added to both sides of the equation to turn $$x+3=10$$ into $$5x+3=4x+10$$?

$$4$$
$$5$$
$$x$$
Correct answer: $$4x$$
$$5x$$

Q4.
$$(−4)$$ is added to both sides of the equation $$9x+4=6$$. What is the resulting equation?

$$x=−4$$
$$9x=6$$
Correct answer: $$9x=2$$
$$5x=2$$

Q5.
$$y=$$ is the solution to the equation $$29=6y−7$$

Correct Answer: 6, six, y=6

Q6.
Solve $$2y−4=−8$$

$$y=6$$
$$y=−6$$
$$y=2$$
Correct answer: $$y=−2$$
$$y=−4$$

Assessment exit quiz

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6 Questions

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

equalities
solutions
variables
Correct answer: expressions

Q2.
What equation is represented by this balance model?

An image in a quiz
$$3x=1$$
$$2x=3$$
$$5x=4$$
$$x+1=x+3$$
Correct answer: $$3x+1=2x+3$$

Q3.
Which additive step will manipulate the equation $$7x−3=2x+18$$ so that it has unknowns on only one side?

Correct answer: $$+(−7x)$$
$$+(3)$$
Correct answer: $$+(−2x)$$
$$+(−18)$$
$$+(−x)$$

Q4.
Add $$3x$$ to both sides of the equation $$x+2=7−3x$$

$$x+5=10−3x$$
$$3x+2=7$$
$$4x+2=7−6x$$
Correct answer: $$4x+2=7$$
$$4x+5=10$$

Q5.
$$x=$$ is the solution to the equation $$5x+21=9x+5$$

Correct Answer: 4, four, x=4, x = 4

Q6.
Solve $$6x−1=7−3x$$

Correct answer: $$x={8\over{9}}$$
$$x={8\over{3}}$$
$$x=−{8\over{9}}$$
$$x={9\over{8}}$$
$$x={6\over{9}}$$