Solving Linear Equations

Maths: Edexcel IGCSE Higher, topic 2.3.1

Solving a Linear Equation

When we rearrange an equation, if we do something to one side, we must do the same to the other side of the equation. To solve the linear equation 6x - 3 = 5 + 2x to find x:

Write equation

Add 3 to both sides

Subtract 2x from both sides

Divide both sides by 4

x = 2 is the solution

Check your answer

So x = 2 does solve the equation.

Solving Linear Equations

Get rid of fractions and brackets first.

Example 1 - Fractions

If the equation has fractions in it, multiply by the denominators (bottom part).
Here we should multiply both sides by (1 - x).

$Remove the fraction by multiplying by the bottom part$

Remove the fraction by multiplying by the bottom part

Example 2 - Brackets

After removing fractions, if the equation has brackets in it, multiply those out before rearranging.
Here we should expand 7(4 - x) → 28 - 7x.

Expand the brackets

Solving Linear Equations Graphically

One line

To solve a linear equation, plot the line and see where it crosses the x axis.
The line y = 2x - 6 crosses the x axis at (2, 0) so the solution is x = 2.

Two lines

For an equation where x is on both sides, plot both lines and find the x-coordinate of the point where they intersect.

Two lines - example

The example shows 2x + 2 = x + 3. Both lines are plotted.

Two lines - example

They intersect at (1, 4) so the solution is x = 1.

Test yourself on Solving Linear Equations

What is 7(4 - x) equal to?
What is 12(x + 2) equal to?
What is 2(x + 8) equal to?
The equation $\frac{x - 2}{x + 6} = 10 - x$ contains an algebraic fraction. What do we get when we multiply both sides by (x + 6)?
The equation $\frac{x + 2}{x + 3} = 10 - x$ contains an algebraic fraction. What do we get when we multiply both sides by (x + 3)?

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