Substitution: Finding the Value

In short: Substitution means putting a number in place of each letter, then working out the answer with the order of operations. If $x=3$, then $2x+1=2\times 3+1=7$.

Before you start

• No sign means multiply: $3a=3\times a$, $ab=a\times b$.
• Powers: $x^2=x\times x$.
• Order of operations: brackets first, then powers, then $\times$ and $÷$, then $+$ and $-$. (The full rules are in Order of Operations.)

How to substitute

Rules and tables

A rule like $y=4x-3$ tells you how to get $y$ from $x$. Substitute each $x$ value to fill in a table.

Notice $y$ goes up by 4 each time $x$ goes up by 1. The number in front of $x$ tells you the jump.

Made-up operations

Test writers love inventing a new symbol and telling you what it means. Just substitute.

The square root $\sqrt{25}$ asks "which number times itself makes 25?" The answer is 5.

Quick summary

• Substitution means replacing each letter with its number.
• Then work it out with the order of operations: brackets, powers, $\times ÷$, $+-$.
• $2x^2$ squares only the $x$. $(2x{)}^2$ squares the whole bracket.
• A rule such as $y=4x-3$ lets you fill in a table of values.
• For a made-up operation like $P\ast Q$, put the first number in for $P$ and the second for $Q$.

Quiz