## Equations

Equations in mathematics are like sentences in English. All equations contain an equals sign, "=". Equations have variables, such as 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:

 x2 = 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 6orx 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.

### 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 = 26Solving the equation:2x + 6 − 6 = 26 − 62x = 20 x = 10 Charlotte's number is 10.