8.6 Rearranging formulae — Learn

Prerequisites: solving one-step equations and using inverse operations.

By the end of this section you can: rearrange a formula by using inverse operations to make a named letter the subject.

Covers: A5.

Learn the method

A formula can be rearranged to make a different letter the subject. The subject is the letter alone on one side.

Undo operations in reverse order, using the same operation on both sides.

From $y=3x+5$, subtract $5$ from both sides, then divide both sides by $3$: $x=(y-5)/3$.

If the subject appears in a product, divide by the other factor. From $A=lw$, divide by $l$ to get $w=A/l$.

Worked example. Make $x$ the subject of $y=5x-2$.

$y+2=5x$ — add $2$ to both sides.

$x=\frac{y+2}{5}$ — divide both sides by $5$.

Watch out. Change both sides of a formula in the same way. Apply each inverse operation to both sides, then substitute back to check.

Progress check

The chapter frame has outer area $(x+6)(x+4)$ and inner area $x(x+2)$. In the next section, you will expand these products to find the frame area.

The frame area will be closer to $10x$ than $12x$ for large $x$.

You should now be able to

• rearrange a formula by using inverse operations to make a named letter the subject.