# KS3. Y9. Solving linear equations

An equation is a statement about the relationship between two algebraic expressions.

It tells us that the two expressions have the same value, i.e. they are equal to each other.

e.g. 4x+3=11, or 9 – 5x = 3

We can solve algebraic equations by finding out the value of the variable (the letter) for which the equations are true.

To do this, it is like playing a game. The aim of the game is to get the letter on its own. The rules of the game are that you can do any arithmetic you like to the expressions as long as you do the same arithmetic to both of the expressions.

e.g. 4x+3 = 11. We can subtract 3 from both expressions to get:

4x = 8 . We can divide both expressions by 4 to get:

x=2.

We have now solved 4x+3=11 and our solution is x=2.

Let’s try some more examples with the teacher:

Now let’s compete exercise 8a on page 112 of the textbook:

On each of the above question the variable (the letter) only appeared on one side of the equation. But it doesn’t matter if it appears on the other side of the equation too. It is just as easy to solve them. Let’s try these with our teacher:

Now we can complete exercise 8B from the textbook: