Solving Equations Literally

Learning Focus

Solve literal equations (formulas with several variables) for a chosen variable.

Big idea

A literal equation has more than one variable. To solve for one of them:

1. Treat the other letters like numbers.
2. Use inverse operations in reverse order (undo addition/subtraction, then multiplication/division).
3. Keep the equation balanced.

The result is a formula for the chosen variable.

Worked example

Solve $P=2\ell+2w$ for $w$.

• Subtract $2\ell$: $P-2\ell=2w$
• Divide by $2$: $w=\dfrac{P-2\ell}{2}$ or $w=\dfrac P2-\ell$

Solve $A=\tfrac12bh$ for $h$: multiply by 2, divide by $b$: $h=\dfrac{2A}{b}$.

Takeaways

• Treat other variables as constants.
• Undo operations in reverse order.
• Literal equations let you reuse a formula for different unknowns.