A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.

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

Many equations, one solution

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

Which of these equations are equivalent to $$x = 5$$?

If $$8x + 4 = 12$$, which of these equations has maintained equality?

Which of these equations are equivalent to  $$12x + 2 = 8x − 6$$?

Which of these is a solution to the equation $$5x − 5 = 9 − 2x$$?

What operation is missing from this diagram?

This bar model represents the initial equation $$2x + 3 = 9$$. What needs to be done to the top bar to maintain equality?

Which of these calculations show '6 plus 3 all multiplied by 2'?

Lucas manipulates the equation $$2x + 8 = 6$$. Which of these equations could he obtain and maintain equality?

Which expression could fill the blank on the right hand side of this equation to maintain equality?

Which of these equations has a solution of $$x = 6$$?

Which of these is a solution to the equation $$18 − 6x = 12 − 4x$$?

Starter Quiz