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

Solution to an equation

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 value of the expressions on both sides of the equals sign when the same. 

The value of the expressions of both sides when the variable is zero.

The value of the variable which makes both sides of the equation equal.

The value of the variable which makes both sides equal to zero.

Which of these best describes what a solution is?

Which of these equations have a solution when $$x = 4$$?

Which of these is a solution to the equation $$3a + 5 = 2a + 2$$?

Which of these equations have no solution?

The graph shows the lines with equations $$y = 2 − 2x$$ and $$y = 2x - 2$$. What is the solution to the equation $$2x − 2 = 2 − 2x$$?

Use the graph to match each equation to its solution.

What is the value of the expression $$5x − 4$$ when $$x = 3$$?

What is the value of the expression $$5x − 4$$ when $$x = −1$$?

The table of values for the equation $$y = 7 − 2x$$ is shown. The missing number is {{ }}.

To find the value of the expression $$21 − 1.5a$$ when $$a = 5$$, you should {{}} the variable $$a$$ for the number 5.

The graph shows 5 lines labelled A, B, C, D and E. Match each line to the equation for that line.

Match  each fraction calculation to its answer.

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