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

The solution to an equality is the value which, when substituted, maintains the equality between the expressions.

Problem solving with 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.

Solving linear equations

The perimeter of this square is $$80$$ units. You can find the value of $$x$$ using the {{}} $$4(7x-8)=80$$.

The perimeter of this square is $$80$$ units. What is the value of $$x$$? $$x=$${{}}.

Find the perimeter of this square. $$P=$${{}}.

An electrician has a call-out fee of £120 and then charges an hourly rate for their work. For a six hour job they charge £480. Calculate their hourly rate.

Sofia thinks of a number. She multiplies it by 6 and then subtracts 24. Sofia multiplies her original number by 4 and adds 6. She gets the same answer both times. Sofia's number is {{}}.

Three children share 65 sweets. Lucas takes 5 more sweets than Jacob does. Izzy takes four times as many sweets as Jacob does. Jacob takes {{}} sweets.

$$4(7x-13)$$ is an {{}} for the perimeter of this square.

Evaluate $$2(3x-4)+2(5x+9)$$ when $$x=6$$. The value of the expression is {{}}.

The solution to the equation $$4(7x-3)=128$$ is $$x=$${{}}.

Laura thinks of a number. She multiplies it by 8 and subtracts 12. Her answer is 60. Laura's number is {{}}.

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