Rearrange formulas

A formula is an equation with several letters. You often need a different letter alone. If $d = r t$ gives distance, you can rearrange it to find the time, without learning a new formula.

Pretend the other letters are numbers. You solve exactly as you would solve

6 = 2 t

Work through it

Solve $A = \frac{1}{2} bh$ for $h$ .

Clear the fraction by multiplying by 2. $2 A = bh$

$h$ is multiplied by $b$ , so divide by $b$ . $h = \frac{2 A}{b}$

Solve $P = 2 l + 2 w$ for $w$ .

Undo the addition. $P - 2 l = 2 w$

Divide by 2. Everything on the left gets divided. $w = \frac{P - 2 l}{2}$

Solve $a x + b = c x + d$ for $x$ .

Gather $x$ terms on the left. $a x - c x = d - b$

Factor out $x$ , the step that's new. $x (a - c) = d - b$

Divide. $x = \frac{d - b}{a - c}$

Watch out for this

From $P = 2 l + 2 w$ , writing $w = P - 2 l - 2$ .

The 2 multiplies $w$ , so you divide by 2. You can't subtract it.

The short version
Treat every other letter as a number. Undo operations until the letter you want is alone.

Your turn

Prefer paper? Print the Linear equations worksheet, with an answer key.

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