• I think of a number, I multiply it by 4, I add 7, the answer is 23.
• I think of a number, I multiply it by 5, I subtract 3 and divide it by 2, I subtract 1. The answer is twice the number that I'm thinking of.
• A rectangle has an area or 1000m² and is composed of two squares. One square has sides which are 10 less than ²/₃ of the other square. what are the side lengths of each square?

Examples of a one step equation

1. Solve the equation 4n = 20.
   This is the same as saying "I think of a number, I multiply it by 4, the answer is 20".
   If you're good with your tables then you can easily find n straight away. There are three ways of solving an equation of this type.
   • The flow chart method:
     n � 4 20
     Working backwards
     20 � 4 5 which is what n is.

   • The balancing method:
     Imagine that the right side of a balance has 20 marbles.
     The other side has 4 boxes containing n marbles. Your aim is to find the number n.
     To keep the balance, you can only take equal amounts on both sides.
     Luckily, both quantities are divisible by 4 so we can find out how many marbles one box is worth. Dividing both sides by 4, we get n=5.
     
     
     
   • Finally, we have the trial and error method which simply means guessing!

   Example
   

2. Solve the equation n + 13 = 27.
   You've got the methods above to do this so it shouldn't be too much of a problem I hope.
   I like the balancing idea though that if you have a box with n marbles and 13 marbles on one side and 27 on the other. You can find how many marbles n is worth by taking the same amount from both sides.

   I'll leave this and two others below as an exercise to you, the answers will be given in the answers page for the algebra exercise at the very end.

   Further Examples
   

3. Solve the equation n - 7 = 14.
4. Solve the equation ⁿ/₃ = 6

Puzzle
You can use your algebra to work this out now!
Joe is 3 years older than his sister, his mother is 6 times as old as him, his father is 6 years older than his mother. The total of their ages is equal to his gran's age who is 73 this year. How old is Joe?