An **equation** states that two expressions are equal in value, eg .

Solving an equation means finding the value or values for which the two expressions are equal. This means equations are not always true. In the example above, , the only correct solution for is 2.

An **identity** is an equation which is always true, no matter what values are substituted. is an identity because will always simplify to regardless of the value of . Identities can be written with the sign ≡, so the example could be written as .

Show that is the solution of the equation

BIDMAS means the multiplication is carried out before the addition:

- Question
Are the following an identity or an equation?

- is an
**equation**because the expression on the left of the equals sign cannot be rearranged to give the equation on the right. The solution to the equation is . - is an
**identity**because when you expand the bracket on the right of the equals sign, it gives the same expression as on the left of the equals sign. - is an
**equation**because the expression on the left of the equals sign cannot be rearranged to give the equation on the right. There is no solution for this equation – no matter what value of is substituted into the equation, the expression on the left will never have the same value as the expression on the right.

- is an