New

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

View unit

Lesson 11 of 17

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

Lesson slides

Download lesson slides

Skip lesson slides

Lesson details

Key learning points

Any linear equation written in the form Ax + B = C can be solved.
Like terms can be collected onto one side of an equation in order to write it in the form Ax + B = C.
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.

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

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Prior knowledge starter quiz

Download quiz pdf

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

Download quiz pdf

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?

$$3x=1$$

$$2x=3$$

$$5x=4$$

$$x+1=x+3$$

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: $$x={8\over{9}}$$

$$x={8\over{3}}$$

$$x=−{8\over{9}}$$

$$x={9\over{8}}$$

$$x={6\over{9}}$$

Lesson appears in

UnitMaths / Solving linear equations

Maths

Show unit

Choose exam board for KS4 Biology

Choose exam board for KS4 Chemistry

Choose exam board for KS4 Combined science

Choose exam board for KS4 Computer Science (GCSE)

Choose exam board for KS4 English

Choose exam board for KS4 French

Choose exam board for KS4 Geography

Choose exam board for KS4 German

Choose exam board for KS4 History

Choose tier for KS4 Maths

Choose exam board for KS4 Music

Choose exam board for KS4 Physical education (GCSE)

Choose exam board for KS4 Physics

Choose exam board for KS4 Religious education (GCSE)

Choose exam board for KS4 Spanish

Rearranging to solve linear equations

Rearranging to solve linear equations

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.In order to maintain in an equation, any manipulation must be applied to both sides of the equation.

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

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

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

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

Q6.Solve $$2y−4=−8$$

Assessment exit quiz

6 Questions

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

Q2.What equation is represented by this balance model?

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

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

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

Q6.Solve $$6x−1=7−3x$$

Lesson appears in

UnitMaths / Solving linear equations

Maths

Q1.
In order to maintain in an equation, any manipulation must be applied to both sides of the equation.

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

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

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

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

Q6.
Solve $$2y−4=−8$$

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

Q2.
What equation is represented by this balance model?

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

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

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

Q6.
Solve $$6x−1=7−3x$$