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:

\[3x + 5 = 3 \times 2 + 5 = 6 + 5 = 11\]

- Question
Say whether each of the following is an identity or an equation

- \[5x + 10 = 3x + 8\]
- \[5x + 10 ≡ 5(x + 2)\]
- \[5x + 10 = 5x +2\]

- This 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 \(x = -1\). - This is an
**identity**because when you expand the bracket on the right of the identity sign, it gives the same expression as on the left of the identity sign. - This 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 \( x\) is substituted into the equation, the expression on the left will never have the same value as the expression on the right.

- This is an