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

Rearranging to solve linear equations

Maths

In this unit, pupils learn how to rearrange an equation to find a specific value that satisfies the equation. In expressions and formulae, pupils use their understanding of rearrangement to change the subject of a formula.

In the prior unit, pupils saw that an arithmetic sequence can be represented graphically and that this is a linear relationship. Any point on the line satisfies this relationship. In this unit, pupils learn how to find a value that satisfies the relationship when the second value is known, without the aid of the graph.

In this unit pupils will learn how to find a value that satisfies a linear relationship when one value is known both with a single step operation, and multiple step operations. A variety of cases are explored including using brackets and rearranging.

Solving linear equations

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

What equation is represented by this balance model?

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

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

$$x=$${{}} is the solution to the equation $$5x+21=9x+5$$

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

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

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

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

$$y=$${{}} is the solution to the equation $$29=6y−7$$

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