Maths:Algebra

Linear equations

An equation is something which has certain solutions. It must involve an '=' sign.

Linear Equations involve only one letter (or 'variable') and the letter mustonly have a power of 1, for example, no squared terms or cubed terms.

To solve them, we must get the letter all on its own by rearranging.

Golden rule: You must always do the same thing to both sides.

One way to think about it is 'letters on one side, numbers on the other.' We do this by 'getting rid of' things that are on the wrong side.

Remember: Every 'term' (collection of letters and/or numbers - 'terms' are separated by + or - signs) has its own + or - sign in front of it.

Here's an example:

Solve 3x - 2 = x + 6

There are more x's on the left so we'll collect x's on the left and numbers on the right:

See if you can solve 7x - 5 = 3x +3.

You should get the answer x = 2.

Try following our simple steps to solve any linear equation:

1. Get rid of any brackets by multiplying out.

2. Get rid of any fractions by multiplying all terms by the denominator.

3. Rearrange by collecting letters on one side and numbers on the other. Remember that every term has its own sign in front of it. Negative terms need to be added to both sides to get rid of them.

4. Divide both sides by the number in front of the variable.

Quadratic equations

Quadratic equations are equations that can be written:

ax² +bx + c = 0

where a, b and c are constants (numbers) and 'a' cannot be zero (-there must be some x²'s!) You might also see them written in the form (x + p)(x + q) = 0 but we?ll come to that later.

You solve them by finding the value(s) of x…