Same Math › Algebra 1 · grades 8–10 › Literal equations
What are literal equations?
A literal equation is a formula with more than one letter, like A = lw or 3x + 2y = 12. Solving it for one letter means getting that letter alone, using the same undo moves as always: subtract to undo adding, divide to undo multiplying. The answer is a new formula, like w = A/l, instead of a number.
- Numbers: divide by 3 to get w alone.
- Letters: divide by l, the same move.
- Circle the letter you're solving for and undo everything around it.
Why schools teach it
One formula, many questions
Algebra 1 students rearrange formulas to highlight a quantity of interest (HSA.CED.A.4): solve d = rt for t to find a travel time, or solve 3x + 2y = 12 for y to graph it.
Kids who freeze at all the letters often relax when they solve a number version side by side. The steps are identical.
At the kitchen table
What to say, and what to skip
Say this
Which letter are we solving for?
Circle it.What's being done to it?
Undo it in reverse order.What would you do if these letters were numbers?
Do the same thing.Does every term get divided?
Yes, the whole side.
Skip this
- Dividing only one term.(12 − 3x) ÷ 2 means both terms get divided: 6 − (3/2)x.
- Undoing in the wrong order.Undo adding and subtracting before multiplying and dividing.
- Expecting a number for an answer.The answer is a formula with the other letters in it.
See it in action
Solving 3x + 2y = 12 for y
Subtract 3x from both sides
2y = −3x + 12Divide every term by 2
y = −(3/2)x + 6Now it's slope-intercept form
y = −(3/2)x + 6
Check with x = 2: 3(2) + 2(3) = 12 ✓.
Free practice sheet
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Parents also ask
Why are they called literal?
From the Latin for letter: they're equations made of letters.
Can there be more than one right-looking answer?
Yes. w = A/l and w = A ÷ l are the same. So are y = 6 − (3/2)x and y = −(3/2)x + 6.
What about formulas with squares, like A = πr²?
Divide by π, then take the square root: r = √(A/π).
Where else does this show up?
Physics and chemistry, constantly: d = rt, F = ma, PV = nRT.