Equations in mathematics are like sentences in English. All equations contain an equals sign, "=". Equations have variables, such as x or p to stand for "unknown" quantities.
The value of these varaibles can often be found by guessing, or using more mathematical methods.
"I think of a number and add 3 to it."
"The result is 8. "
"What is the number?"


Most people can easily work out that the number is 5.
In mathematics, we would write an equation x + 3 = 8, where x stands for the number. We would then solve the equation to find the value of the number (x). This sounds a long way of doing things but many equations are more difficult to solve than the one above.
Some equations have more than one answer:
x^{2} = 9

x could be 3 or 3

Some equations have more than one variable:
x + y = 9

There are lots of possible answers.
e.g. x could be 3 and y could be 6 or x could be 4 and y could be 5.

There are several types of equations and several methods of solving them. These are studied in more detail in later years.
Simple Equations
 These equations are sometimes called linear equations.
 These equations usually have one variable, like the problem above and only one answer.
 Equations can sometimes be solved by working out the answer in your head. (Guess and check.) This method usually works for simple equations only.
 The aim when solving an equation is find the value of the variable that makes the equation true.
 Always check that the answer is correct by substituting your answer back into the equation.
Examples 
Method One (Guess and check) 
Method Two (balancing both sides)

x + 7 = 15

Guess: What is added to 7 to give 15? The answer must be x = 8.

x + 7 = 15
x + 7 − 7 = 15 − 7 (subtract 7 from both sides)
x = 8

Check: Left hand side = 8 + 7 = 15 Right hand side = 15
Therefore the answer is correct.

g − 5 = 11

Guess: What number would you subtract 5 from to give 11? The answer must be g = 16.

g − 5 = 11
g − 5 + 5 = 11 + 5 (add 5 to both sides)
g = 16

Check: Left hand side = 16 − 5 = 11 Right hand side = 11
Therefore the answer is correct.

3w = 15

Guess: What number would you multiply 3 by to give 15? The answer must be w = 5. 
3w = 15
^{3w}⁄_{3} = ^{15}⁄_{3} (divide both sides by 3)
w = 5

Check: Left hand side = 3 x 5 = 15 Right hand side = 15
Therefore the answer is correct.

p ÷ 8 = 4 
Guess: What number would you divide by 8 to give 4? The answer must be w = 32. 
p ÷ 8 = 4
p ÷ 8 x 8 = 4 x 8 (multiply both sides by 8)
p = 32

Check: Left hand side = 32 ÷ 8 = 4 Right hand side = 4
Therefore the answer is correct.

2p + 5 = 17 
Guess: What number would you multiply by 2 and add 5 to give 17? The answer must be w = 6. 
2p + 5 = 17 2p + 5 − 5 = 17 − 5 (subtract 5 from both sides) 2p = 12 2p ÷ 2 = 12 ÷ 2 (divide both sides by 2) p = 6

Check: Left hand side = 2 × 6 + 5 = 17 Right hand side = 17
Therefore the answer is correct.

Word Problems
Many word problems can be solved by making equations and solving them. The general way to approach these problems is:
 Let a variable or letter be the unknown quantity in the problem.
 Make up an equation from the information in the problem.
 Solve the equation.
Example 
Answer 
Charlotte thinks of a number, doubles it and adds 6.
The result is 26.
What is her number?

Let the unknown number be x. The equation is: 2x + 6 = 26 Solving the equation: 2x + 6 − 6 = 26 − 6 2x = 20 x = 10
Charlotte's number is 10.

