Solving linear equations

Foundation and Higher

The idea

Solve an equation by doing the same to both sides until $x$ is on its own. With $x$ on both sides, collect it on the side where it has the larger coefficient.

Expand any brackets.
Collect the $x$ terms on one side and numbers on the other: $5x - 3 = 2x + 9$ gives $3x = 12$ .
Divide: $x = 4$ . Substitute back to check.

Watch out Whatever you do to one side, do to the whole of the other side.

See it worked

Worked exampleCalculator allowed2 marks

Solve 6x + 5 = 47.

$6x=42$
Subtract 5 from each side: 6x = 42.
Divide each side by 6: x = 7.

Answer $7$

Your turn

Question 1Non-calculator6 marks

Solve each equation.

(a) Solve $4x + 7 = 27$

(b) Solve $5(y - 2) = 35$

Question 2Non-calculator5 marks

$\frac{x-6}{3}+\frac{x+3}{2}=9/2$ .

(a) Solve for x.

(b) Find the value of 2x - 1.

Question 3Non-calculator6 marks

Show clear algebraic working.

(a) Solve $\dfrac{x + 4}{3} - \dfrac{x - 2}{4} = 2$ . You must show your working.

(b) The mean of the four expressions $2x + 1$ , $3x - 2$ , $x + 7$ and $10$ is equal to $3x - 1$ . Find the value of $x$ . You must show your working.

In past papers

188 official questions in 154 papers since 2017. The latest:

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