An equation is a statement with an equals sign, stating that two expressions are equal in value, for example \(3x + 5 = 11\)
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 equal \(5x\) 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 \(3x + 5 = 11\)
BIDMAS means the multiplication is carried out before the addition:
\[3x + 5 = 3 \times 2 + 5 = 6 + 5 = 11\]
Say whether each of the following is an identity or an equation