Printable pre-algebra, algebra and geometry worksheets

Literal Equations Worksheet Generator

Make printable literal equation practice – solve A = lw for w, d = rt for t or 2x + 3y = 12 for y – with an answer key on its own page.

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A literal equation worksheet gives practice in solving equations that contain two or more letters, such as A = lw, for one chosen letter. This literal equations worksheet generator makes a printable algebra worksheet of these problems right in your web browser. It is free and needs no sign-up, and nothing is uploaded: the problems are made on your device.

You choose the problem types, the difficulty and the number of problems. Then you print the sheet or save it as a PDF, with an answer key on a separate page if you want one. Teachers and students can use it for homework, class practice or review, and everything you make is free for commercial use, such as Teachers Pay Teachers resources. Each new set of problems is different, so you can practise as many times as you need.

Literal equations worksheet example

How to use the literal equations worksheet generator

  1. Under Problem types, tick one or more boxes. When several are ticked, the problems are shared out evenly and grouped by type. Two types are ticked when the page opens: Literal equations: two steps and Solve formulas for a variable.
  2. Under Difficulty, choose Easy, Medium or Hard.
  3. Under Number of problems, choose 6, 8, 10, 12, 15, 20, 24 or 30.
  4. Open More options to set the Columns (Automatic, 1, 2 or 3), the Paper size (Letter or A4), a Worksheet title, and whether to show a Name and date line. The Answer key on a separate page box is on by default; untick it if you do not want a key.
  5. Check the preview on the right. It shows the sheet as it will print.
  6. Click Show answers to see each answer under its problem in the preview. Click again to hide them.
  7. Click New worksheet for a fresh random set of problems with the same settings.
  8. Click Print / Save as PDF to open the print dialog. Choose “Save as PDF” there to make a PDF file.

The generator remembers your settings for your next visit, unless you open a shared link, which uses that link’s settings. Copy link copies a link that opens exactly the same worksheet again. It works on phones and tablets, but printing needs a printer or the Save as PDF option.

What is a literal equation

A literal equation is an equation with two or more letters (variables). Solving it for one letter means getting that letter alone on one side of the equals sign.

Formulas are literal equations. The formula A = lw has three letters, and you can solve it for any one of them. Solved for w, it becomes w = A/l. The formula I = Prt solved for r gives r = I/(Pt), and d = rt solved for t gives t = d/r.

How do you solve a literal equation for a variable

Treat every other letter as if it were a number, and undo the operations attached to the letter you want. Use inverse operations: addition is undone by subtraction, and multiplication is undone by division. Undo addition or subtraction first, then multiplication or division.

For example, to solve ax + b = c for x:

  1. Subtract b from both sides: ax = c − b.
  2. Divide both sides by a: x = (c − b)/a.

Standard form works the same way. To write 2x + 3y = 12 in slope-intercept form, solve for y:

  1. Subtract 2x from both sides: 3y = −2x + 12.
  2. Divide every term by 3: y = −(2/3)x + 4.

Perimeter P = 2l + 2w solved for l works in the same two steps: subtract 2w from both sides to get 2l = P − 2w, then divide by 2 to get l = (P − 2w)/2. Always do the same thing to both sides, and check that the letter you wanted is alone on one side at the end.

Which formulas are on the worksheets?

The Solve formulas for a variable type draws on 32 real formulas from geometry, science and money, such as C = πd, V = (1/3)πr²h, F = (9/5)C + 32, K = (1/2)mv² and A = P(1 + rt). Solving V = (1/3)πr²h for h, for example, gives h = 3V/(πr²), and solving A = P(1 + rt) for t gives t = (A − P)/(Pr).

Sample problems from this generator

  1. z = as + n Solve for s Answer: s = z − na
  2. m = xd − v Solve for d Answer: d = m + vx
  3. v = u + at Solve for t Answer: t = v − ua
  4. V = 13Bh Solve for h Answer: h = 3VB

Frequently asked questions

Why learn literal equations?

Many formulas in science, geometry and finance are literal equations. Rearranging them lets you find whichever quantity you know. For example, if you know the distance and the rate, d = rt solved for t gives the time.

How do you solve a formula for a variable that appears twice?

Collect the terms that contain that variable on one side, then factor it out. For ax + bx = c, factor to get x(a + b) = c, then divide to get x = c/(a + b). For dt + t = p, factor to get t(d + 1) = p, so t = p/(d + 1).

Can I use the literal equations worksheets I make in my tutoring business or my TpT store?

Yes. Everything you make here is royalty-free for personal, classroom and commercial use, including Teachers Pay Teachers, Etsy printables, KDP workbooks and print-on-demand products. No credit is required. The only thing you may not do is copy the generator or the site itself to run a competing service. See the terms.

What does the “Solve a formula, then evaluate” type ask?

First solve the formula for the letter shown, then put in the given values. For example: solve A = lw for w, then find w when A = 40 and l = 8. The answer key shows both parts: w = A/l; w = 5.

Is there a cost or an account needed?

No. The tool is free, needs no sign-up, and nothing is uploaded.

How do I get a PDF or a printed copy?

Click Print / Save as PDF. Your browser’s print dialog opens. Choose a printer, or choose “Save as PDF” to make a file. When printed, the answer key starts on a new page after the worksheet.