Basic Algebra

Algebra follows the same rules you have used with numbers, but because the number is unknown it can look very different.

Variables:

If we do not know the value of a number, we can call it $x$, $a$ or whichever letter we like.

Expressions

$$3\times 5=15$$

If we multiply two numbers, such as 3 and 5, we can write the answer.

$$3\times x$$

We cannot do this with algebra because we do not know what the number is.

$$3\times x=3x$$

The $\times$ and the $x$ look very similar! Thankfully we never have to show the (\times \) sign in algebra.

$$3\times x+10=3x+10$$

If we added 10 to $3x$ we can write this as $3x+10$

Substitution

If we find out what number the letter represents, we can find the value of an expression by using substitution.

$$3x+10$$

If $x=4$ we can find the value of $3x+10$ by replacing the x for 4. But be careful! We must first put back in the times sign.

$$3\times x+10$$

$$3\times 4+10$$

$$12+10$$

$$22$$

Equations

An equation is where we have two expressions equal to each other. You can spot an equation because it will have an equals sign.

$$3x+5=14$$

In this equation, x is a value that can be found.

Formula

A formula is a statement linking more than one variable (can be real-world).

$$A=\frac{1}{2}\times b\times h$$

You might recognise this formula as the area of a triangle. Each letter means something. $b$ is the base of the triangle and $h$ is the height.

Identity

An identity is a statement that is true for all values of the variable.

$$3x=x+x+x$$

This identity is true for all values of $x$.

$$3\times 5=5+5+5$$

$$3\times 10=10+10+10$$

$$3\times 999=999+999+999$$

We can show identities with three equals signs (but they will probably use two in your exam).

$$3x\equiv x+x+x$$