CMClearMathAcademy

Literal Equations

A free Algebra I lesson from the “Algebra Foundations” unit, with a worked example and practice problems including step-by-step solutions.

A literal equation has two or more variables. Solving for one variable means isolating that variable so the formula is ready to use in a new situation.

What you'll learn

Why it matters: Science labs, shop drawings, finance sheets, and engineering notes often rearrange one formula for whichever variable must be measured next.

Worked example

Problem. Solve A = lw for w.

  1. The target variable is w.
  2. w is multiplied by l, so divide both sides by l.
  3. w = A/l.

Answer: w = A/l

Practice problems

1. Solve A = lw for w.

Choices: w = A/l · w = Al · w = l/A · w = A - l

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve A = lw for w.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. w is multiplied by l.
  4. Divide both sides by l.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: w = A/l

2. Solve y = x + b for b. Enter the expression for b.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve y = x + b for b. Enter the expression for b.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Subtract x from both sides.
  4. b = y - x.
  5. Check the result by substituting or estimating: the response should match y - x and make sense in the original problem.

Answer: y - x

3. Solve p = 2l + 2w for p.

Choices: p = 2l + 2w · p = l + w · p = 4lw · p = 2(l - w)

Show solution
  1. Warm-up: First identify exactly what the question is asking: Solve p = 2l + 2w for p.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. p is already isolated.
  4. No rearranging is needed.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: p = 2l + 2w

4. Solve d = rt for t.

Choices: t = d/r · t = dr · t = r/d · t = d - r

Show solution
  1. Core Practice: First identify exactly what the question is asking: Solve d = rt for t.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. t is multiplied by r.
  4. Divide both sides by r.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: t = d/r

5. Solve C = 2pi r for r.

Choices: r = C/(2pi) · r = 2pi/C · r = C - 2pi · r = 2Cpi

Show solution
  1. Core Practice: First identify exactly what the question is asking: Solve C = 2pi r for r.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. r is multiplied by 2pi.
  4. Divide both sides by 2pi.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: r = C/(2pi)

Practice this interactively with instant feedback and an AI tutor.

Practice Literal Equations Take the free placement check

More Algebra I lessons