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Preparing to solve two step linear equations

I can understand that an equation needs to be in a format to be ready to be solved, through collecting like terms on each side of the equation.

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Lesson 9 of 17

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Year 8

Preparing to solve two step linear equations

I can understand that an equation needs to be in a format to be ready to be solved, through collecting like terms on each side of the equation.

Download all

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Lesson details

Key learning points

An equation with both a multiplicative and additive step can be solved using a bar model.
The solution can be formalised using algebra.
Any linear equation written in the form Ax + B = C can be solved.
Any linear equation can be written in the form Ax + B = C by collecting like terms.

Keywords

Like terms - Like terms are terms that have the same set of variables and corresponding exponents

Common misconception

Pupils can be unsure which values to add and which to subtract when collecting like terms.

Rewrite the equation with like terms grouped together before combining like terms.

This is a chance to consolidate the skills of collecting like terms, expanding brackets and forming expressions for perimeter. Challenge pupils to write the most complicated equation they can which can still be written as ax + b = c

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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 solution to the equation $$x + 16 = 11$$ is $$x$$ = .

Correct Answer: −5, - 5, -5, − 5

Q2.
The solution to $$12x =−48$$ is $$x=$$ .

Correct Answer: −4, - 4, -4, − 4

Q3.
terms are terms that have the same set of variables and corresponding exponents.

Correct Answer: Like, like

Q4.
Match each term with a like term.

Correct Answer:$$5x^2$$,$$−3x^2$$

Correct Answer:$${3x^2}y$$,$${67x^2}y$$

Correct Answer:$$2xy^2$$,$${3y^2}x$$

Correct Answer:$$7.5x$$,$$−{1\over5}x$$

Correct Answer:$${1\over 4}y$$,$$−y$$

Correct Answer:$$−xy$$,$$2.3yx$$

Q5.
Fully simplify $$5x − 9x + 3x − x$$

$$−8x$$

Correct answer: $$−2x$$

$$−1x−x$$

$$6x$$

$$18x$$

Q6.
Which of these is equivalent to $$−4(2x − 5)$$?

$$−6x − 9$$

$$−8x −20$$

$$−8x − 5$$

$$−8x + 5$$

Correct answer: $$−8x + 20$$

Assessment exit quiz

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6 Questions

Q1.
Which equations are represented by this bar model?

$$2x + 6 = 58$$

$$6x + 12 =58$$

Correct answer: $$6x + 18 = 58$$

$$2(3x+6) = 58$$

Correct answer: $$3(2x+6) = 58$$

Q2.
Which equations are represented by this bar model?

$$6x + 7 = 30$$

Correct answer: $$7x + 12 = 39$$

$$4(2x + 3) = 39$$

$$3(2x + 3) + x + 2 = 39$$

Correct answer: $$2(2x + 3) + 3(x + 2) = 39$$

Q3.
For this bar model, there is a solution to the equation $$5x + 15 = 55$$ when $$x =$$ .

Correct Answer: 8, eight

Q4.
Which of these are equivalent to the equation $$7(x − 1) − 3(x − 1) = 50$$ ?

$$7x − 7 - 3x − 3 = 50$$

$$4x = 50$$

Correct answer: $$4x − 4 = 50$$

Correct answer: $$4(x − 1) = 50$$

$$10(x − 1) =50$$

Q5.
Which of these is equivalent to the equation $$5(2x+1) − 3(3x − 2) = 50$$ ?

$$x − 1 = 50$$

Correct answer: $$x + 11 = 50$$

$$2x − 1 = 50$$

$$2(2x + 1) = 50$$

$$2(5x − 1) =50$$

Q6.
This shape is made out of a rectangle and two rhombuses (one on each end of the rectangle). Which of these is the correct expression for the perimeter of the shape?

$$4x$$

$$8x$$

$$10x + 10$$

Correct answer: $$12x + 20$$

$$14x + 30$$

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UnitMaths / Solving linear equations

Maths

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Preparing to solve two step linear equations

Preparing to solve two step linear equations

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.The solution to the equation $$x + 16 = 11$$ is $$x$$ = .

Q2.The solution to $$12x =−48$$ is $$x=$$ .

Q3. terms are terms that have the same set of variables and corresponding exponents.

Q4.Match each term with a like term.

Q5.Fully simplify $$5x − 9x + 3x − x$$

Q6.Which of these is equivalent to $$−4(2x − 5)$$?

Assessment exit quiz

6 Questions

Q1.Which equations are represented by this bar model?

Q2.Which equations are represented by this bar model?

Q3.For this bar model, there is a solution to the equation $$5x + 15 = 55$$ when $$x =$$ .

Q4.Which of these are equivalent to the equation $$7(x − 1) − 3(x − 1) = 50$$ ?

Q5.Which of these is equivalent to the equation $$5(2x+1) − 3(3x − 2) = 50$$ ?

Q6.This shape is made out of a rectangle and two rhombuses (one on each end of the rectangle). Which of these is the correct expression for the perimeter of the shape?

Lesson appears in

UnitMaths / Solving linear equations

Maths

Q1.
The solution to the equation $$x + 16 = 11$$ is $$x$$ = .

Q2.
The solution to $$12x =−48$$ is $$x=$$ .

Q3.
terms are terms that have the same set of variables and corresponding exponents.

Q4.
Match each term with a like term.

Q5.
Fully simplify $$5x − 9x + 3x − x$$

Q6.
Which of these is equivalent to $$−4(2x − 5)$$?

Q1.
Which equations are represented by this bar model?

Q2.
Which equations are represented by this bar model?

Q3.
For this bar model, there is a solution to the equation $$5x + 15 = 55$$ when $$x =$$ .

Q4.
Which of these are equivalent to the equation $$7(x − 1) − 3(x − 1) = 50$$ ?

Q5.
Which of these is equivalent to the equation $$5(2x+1) − 3(3x − 2) = 50$$ ?

Q6.
This shape is made out of a rectangle and two rhombuses (one on each end of the rectangle). Which of these is the correct expression for the perimeter of the shape?