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Solving two step linear equations

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Lesson details

Learning outcome

I can see that when an additive step and a multiplicative step are required to solve an equation, the order of operations will not affect the solution.

Key learning points

  1. When an equation is in the form Ax + B = C you can solve by first subtracting B from both sides.
  2. When an equation is in the form Ax + B = C you can solve by first dividing both sides by A.
  3. These two options give the same solution.
  4. In any particular situation one way may be more efficient than the other and it useful to think carefully about this.

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.

Teacher tip

Ask pupils to solve the same equation twice using two different methods. Get them to compare the methods and their efficiency. This will better prepare pupils for more complex equations.

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

Correct Answer: equal, Equal

Q2.
Work out the value of $$13+7+(−7)$$

$$6$$
$$7$$
Correct answer: $$13$$
$$20$$

Q3.
Work out the value of $${20 \over 4}$$

$$4$$
Correct answer: $$5$$
$$16$$
$$20$$
$$80$$

Q4.
Solve the equation $$x + 9 = 21$$

$$x=9$$
Correct answer: $$x=12$$
$$x=21$$
$$x=30$$

Q5.
Solve the equation $$5x = 15$$

Correct answer: $$x=3$$
$$x=5$$
$$x=10$$
$$x=75$$

Q6.
Solve the equation $$7x = 3$$

$$x=−4$$
Correct answer: $$x={3\over7}$$
$$x={7\over3}$$
$$x=21$$
It can't be solved because $$7$$ is not divisible by $$3$$

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
The solution to an equation is the value which, when substituted, maintains the between the two expressions.

Correct Answer: equality, Equality

Q2.
Which is the most useful additive first step to apply to both sides when solving $$7y − 3=18$$?

$$−3$$
Correct answer: $$+3$$
$$−7$$
$$−18$$

Q3.
Solve $$3y + 7 = 19$$

$$y=3$$
$$3y=12$$
Correct answer: $$y=4$$
$$y=12$$

Q4.
Which is the most useful multiplicative first step to apply to both sides when solving $$6y−12=18$$?

$$\div 2$$
$$\div 3$$
Correct answer: $$\div 6$$
$$\times 3$$
$$\times 6$$

Q5.
Match each equation to its solution.

Correct Answer:$$2x+3=4$$,$$x={1\over2}$$

$$x={1\over2}$$

Correct Answer:$$3x+2=4$$,$$x={2\over3}$$

$$x={2\over3}$$

Correct Answer:$$2x+4=3$$,$$x=−{1\over2}$$

$$x=−{1\over2}$$

Correct Answer:$$3x+4=2$$,$$x=−{2\over3}$$

$$x=−{2\over3}$$

Correct Answer:$$4x+3=2$$,$$x=−{1\over4}$$

$$x=−{1\over4}$$

Correct Answer:$$4x+2=3$$,$$x={1\over4}$$

$$x={1\over4}$$

Q6.
$$x=$$ is the solution to the equation $${x\over8}+{1\over4}={1\over2}$$

Correct Answer: 2, two, x=2

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