1.6Literal Equations & Formulas
A literal equation contains two or more variables. Solving for one variable uses the exact same inverse-operation strategy as solving for a number — the answer just stays in terms of letters.
Why This Matters
Literal equations are the foundation of every science formula. Rearranging d = rt for t, or F = ma for a, is something you'll do constantly in Physics, Chemistry, and engineering — this lesson makes that automatic.
Workbook
Lesson, vocabulary, worked examples, and practice problems.
Essential Question
How do you isolate one variable in an equation that contains several variables — and why is this skill essential in science, engineering, and everyday problem-solving?
Lesson Overview
A literal equation is an equation with two or more variables, such as A = lw or d = rt. Formulas from geometry, physics, and finance are all literal equations. To solve a literal equation for a specific variable, treat every other variable as if it were a number and use inverse operations to isolate the target variable — exactly as you would in a one-step or multi-step equation. The result is an expression (not a single number) that shows the target variable in terms of the others.
Worked Examples
Solve d = rt for r.
r is multiplied by t → divide both sides by t:
r = d/t
Check: if d=60, t=3, r=20. 60=20×3 ✓
Solve A = lw for w.
w is multiplied by l → divide both sides by l:
w = A/l
Check: if A=24, l=6, w=4. 24=6×4 ✓
Solve P = 2l + 2w for l.
Subtract 2w: P − 2w = 2l
Divide by 2: l = (P − 2w)/2
Check: P=20, w=3 → l=7. 20=2(7)+2(3) ✓
Solve A = ½bh for h.
Multiply both sides by 2: 2A = bh
Divide by b: h = 2A/b
Check: A=15, b=5 → h=6. 15=½(5)(6) ✓
Solve F = (9/5)C + 32 for C.
Subtract 32: F − 32 = (9/5)C
Multiply by 5/9: C = (5/9)(F − 32)
Check: F=212 → C=100 (boiling point) ✓
Guided Practice
Guided Practice Video: Literal Equations & Formulas
Watch the guided practice walkthrough for literal equations and formulas, then complete the problems below.
Video by Sang Real Math
Watch on YouTube ↗Answers are in the Answer Key section.
Solve V = lwh for h.
Hint: h is multiplied by l and w. Divide both sides by lw.
Solve P = 2l + 2w for w.
Hint: Subtract 2l from both sides first, then divide by 2.
Solve C = 2πr for r.
Hint: r is multiplied by 2π. Divide both sides by 2π.
Solve A = ½bh for b.
Hint: Multiply both sides by 2 to clear the fraction, then divide by h.
Solve y = mx + b for x.
Hint: Subtract b from both sides first, then divide by m.
Key Vocabulary
Literal Equation
An equation that contains two or more variables.
Example: A = lw, d = rt, F = (9/5)C + 32
Formula
A literal equation that describes a mathematical relationship between quantities.
Example: A = ½bh (area of a triangle)
Solve for a Variable
To rearrange an equation using inverse operations so the specified variable stands alone on one side.
Example: Solve A = lw for w → w = A/l
Subject of a Formula
The variable expressed alone on one side of the formula.
Example: In A = lw, A is the subject.
Practice Questions
Interactive Practice — 5 Questions
Solve d = rt for r.
Solve A = ½bh for h.
Solve P = 2l + 2w for l.
Solve F = (9/5)C + 32 for C.
Solve y = mx + b for x.
Independent Practice
Answers are in the Answer Key section.
Independent Practice
Solve d = rt for t.
Solve A = lw for l.
Solve I = Prt for r.
Solve V = lwh for l.
Solve 2x + 3y = 12 for y.
Common Mistakes
Treating other letters as numbers — e.g., solving A = lw for l by writing l = A − w.
Treat every letter except the target as a constant. Divide both sides by w: l = A/w.
Undoing operations in the wrong order — e.g., solving v = u + at for t by dividing by a before subtracting u.
Follow reverse PEMDAS: undo addition/subtraction first, then multiplication/division.
Forgetting to apply the operation to the entire side — e.g., solving P = 2l + 2w for l by subtracting only 2 instead of 2w.
Subtract the entire term 2w: P − 2w = 2l, then divide by 2.
Forgetting to clear fractions first — e.g., in A = ½bh, dividing by b before multiplying by 2.
Multiply by 2 first: 2A = bh. Then divide by b: h = 2A/b.
Math Tips
Treat every variable you are not solving for as if it were a constant number.
Undo addition/subtraction before multiplication/division (reverse PEMDAS).
If the target variable is in a fraction, multiply both sides by the denominator first to clear it.
Always check by substituting simple numbers into both the original and rearranged formulas.