How To Solve Simple Linear Equations

Simple linear equations can appear on GCSE examination papers across all three tiers, so are an absolute must for understanding.

Linear equations tend to be of the form:

6x + 5 = 10 or maybe even 5x + 4 = 7x + 10

In order to solve linear equations we need to collect like terms together on either side., so for our first example 6x + 5 = 10, we would have 6x = 10 - 5 so that 6x =5 and hence x = 5/6.

Linear equations can sometimes involve brackets that will need to be expanded prior to solving. The following worked example illustrates how a student would proceed with solving such an equation.

Given 7(k + 3)=4k + 20 what is the value of k?

Expanding bracket: 7k + 21 = 4k +20

Collecting like terms: 7k - 4k = 20 - 21

Simplifying: 3k = - 1

Solving: k = - 1/3 which is the value we require.

To recap... Rules for solving linear equations:

1. Expands any brackets, if any appear in an equation
2. Do same operation to both sides of the equation
3. Collect like terms together
4. Simplify expression
5. Solve.