Algebra
Single-variable equations
Literal equations and formulas
20 practice questions
2 video lessons
Theory + worked examples
Theory
A literal equation (or formula) has more than one variable. To solve for one:
- Treat the other letters as constants.
- Use inverse operations on both sides.
- Isolate the target variable.
The steps are the same as any equation — only the “numbers” are letters.
Isolate the target variable.
Rearranged formulas.
The idea:
\[A=lw\ \Rightarrow\ w=\dfrac{A}{l}\]
Whatever undoes the operation on the target variable, apply to both sides.
How to rearrange a formula
- Identify the variable to isolate.
- Treat the rest as constants.
- Undo operations with inverses, both sides.
- Write the target variable alone.
Example 1 — Solve for a factor
Solve \(A=lw\) for \(w\).
Solution
Divide both sides by \(l\).
| \(w\) | \(=\) | \(\dfrac{A}{l}\) |
Example 2 — A rate formula
Solve \(d=rt\) for \(t\).
Solution
Divide by \(r\).
| \(t\) | \(=\) | \(\dfrac{d}{r}\) |
Example 3 — Two steps
Solve \(P=2l+2w\) for \(l\).
Solution
Subtract, then divide.
| \(P-2w\) | \(=\) | \(2l\) |
| \(l\) | \(=\) | \(\dfrac{P-2w}{2}\) |
Example 4 — Solve a line for x
Solve \(y=mx+b\) for \(x\).
Solution
Undo the addition, then the multiplication.
| \(y-b\) | \(=\) | \(mx\) |
| \(x\) | \(=\) | \(\dfrac{y-b}{m}\) |
Common pitfalls
Apply operations to the whole side, not just one term.
Treat other letters as numbers while solving.
Divide the entire other side when isolating.
Frequently asked questions
What is a literal equation?
An equation with several variables, such as a formula.
How do you solve \(A=lw\) for \(w\)?
Divide both sides by \(l\): \(w=\dfrac{A}{l}\).
Is rearranging a formula different from solving an equation?
No — the same inverse-operation steps apply.
Why treat other variables as constants?
Because you are isolating just one of them.
More in Single-variable equations