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Linear Equations

A linear equation is an equation in which each term is either a constant or the product of a constant times the first power of a variable. In simple terms it is a mathematical sentence in which you can see only one letter (which might appear more than once) but there will be no powers (squared, cubed etc). Here is an example of a simple linear equation:

2x + 7 = 15

This equation can be "solved" to find which value is represented by the letter x.

The eQuation Generator above can make up unlimited equations for you to practise solving. You can change the options so that one of five different types of equation is displayed.

Here are examples showing a good way to solve equations by thinking of the two sides of the equation as two sides of a balance. The equation will remain balanced only if you do the same thing (multiply, divide add or subtract) to both sides.

Type 1

3x = 12
Divide both sides by 3
x = 4

By doing the same thing to both sides of the equation you can find what one x is equal to.

Self marking exercise

Type 2

4x - 3 = 13
Add 3 to both sides
4x = 16
Divide both sides by 4
x = 4

Self marking exercise

Type 3

5x + 3 = 3x + 15
Subtract 3 from both sides
5x = 3x + 12
Subtract 3x from both sides
2x = 12
Divide both sides by 2
x = 6

Self marking exercise

Muscles

Type 4

2(3x - 4) + 1 = 5
Subtract 1 from both sides
2(3x - 4) = 4
Divide both sides by 2
3x - 4 = 2
Add 4 to both sides
3x = 6
Divide both sides by 3
x = 2

Another method:

2(3x - 4) + 1 = 5
First multiply out (expand) the brackets
6x - 8 + 1 = 5
Collect together like terms
6x - 7 = 5
Add 7 to both sides
6x = 12
Divide both sides by 6
x = 2

Self marking exercise

Type 5

3(3x - 2) + 8 = 4x + 3
First multiply out (expand) the brackets
9x - 6 + 8 = 4x + 3
Collect together like terms
9x + 2 = 4x + 3
Subtract 2 from both sides
9x = 4x + 1
Subtract 4x from both sides
5x = 1
Divide both sides by 5
x = 0.2

Self marking exercise

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