Substitution

In a Nutshell

Substitution means swapping each letter for a number and then working out the answer — algebra meets arithmetic.

When you know the value of a variable, you can substitute it into an expression. Replace every occurrence of the letter with the given number, then calculate the result using the normal order of operations (BIDMAS).

For example, if $x = 4$ , then

3x + 5 = 3 \times 4 + 5 = 12 + 5 = 17

Be especially careful with squared terms and negative numbers:

\text{If } x = -2, \quad x^2 = (-2)^2 = 4

Value of x

The table shows the value of $3x + 1$ for different values of $x$ . Enter a new value and press "Add column" to extend the table.

Watch it work

Question: Given $a = 3$ and $b = 5$ , find the value of $2a + 3b$ .

Have a go

Q1. If $x = 6$ , find $4x - 7$ .

Q2. If $y = -3$ , find $y^2 + 2y$ .

Q3. If $a = 2$ and $b = 4$ , find $5a - b + 3$ .

Q4. If $p = 10$ , find $\dfrac{p}{2} + 8$ .