An equation states that two expressions are equal in value, eg \(3x + 5 = 11\).

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, \(3x + 5 = 11\), the only correct solution for \(x\) is 2.

An identity is an equation which is always true, no matter what values are substituted. \(2x + 3x = 5x\) is an identity because \(2x + 3x\) will always simplify to \(5x\) regardless of the value of \(x\). Identities can be written with the sign ≡, so the example could be written as \(2x + 3x ≡ 5x\).

Show that \(x = 2\) is the solution of the equation \(3x + 5 = 11\)

\(3x + 5 = 3 \times 2 + 5 = 6 + 5 = 11\)