Worksheet Solving Literal Equations Worksheet - Free Printable

Absolutely! Let's solve each of these literal equations step-by-step. "Solving for a variable" means isolating that variable on one side of the equation using algebraic operations.

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1. V = Bh; solve for B

We want to isolate B.

- Divide both sides by h:

> B = V/h

✔ Final Answer: B = V/h

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2. d = c/r; solve for c

We want to isolate c.

- Multiply both sides by r:

> c = d·r

✔ Final Answer: c = dr

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3. L = A/W; solve for W

We want to isolate W.

- Multiply both sides by W:

> L·W = A

- Now divide both sides by L:

> W = A/L

✔ Final Answer: W = A/L

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4. x = (1/2)r²w; solve for w

We want to isolate w.

- Multiply both sides by 2 to eliminate the fraction:

> 2x = r²w

- Now divide both sides by r²:

> w = 2x / r²

✔ Final Answer: w = 2x / r²

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5. V = (b²h)/3; solve for h

We want to isolate h.

- Multiply both sides by 3:

> 3V = b²h

- Divide both sides by b²:

> h = 3V / b²

✔ Final Answer: h = 3V / b²

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6. F = (kE₁E₂)/d²; solve for E₁

We want to isolate E₁.

- Multiply both sides by d²:

> F·d² = kE₁E₂

- Now divide both sides by kE₂:

> E₁ = (F·d²) / (kE₂)

✔ Final Answer: E₁ = (Fd²)/(kE₂)

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7. 3w = (1/2)z - 5; solve for z

We want to isolate z.

- Add 5 to both sides:

> 3w + 5 = (1/2)z

- Multiply both sides by 2 to eliminate the fraction:

> z = 2(3w + 5) = 6w + 10

✔ Final Answer: z = 6w + 10

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8. 5ax - 2b = cx - c; solve for b

We want to isolate b.

- Move all terms *not* containing b to the right side.

Subtract 5ax from both sides:

> -2b = cx - c - 5ax

- Multiply both sides by -1:

> 2b = -cx + c + 5ax

Or better: 2b = 5ax - cx + c

- Factor the right side if possible (optional):

> 2b = x(5a - c) + c

- Divide both sides by 2:

> b = [x(5a - c) + c] / 2

✔ Final Answer: b = (5ax - cx + c)/2
*(or factored: b = [x(5a - c) + c]/2)*

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9. 3x + a = b; solve for x

We want to isolate x.

- Subtract a from both sides:

> 3x = b - a

- Divide both sides by 3:

> x = (b - a)/3

✔ Final Answer: x = (b - a)/3

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10. v = V + gt; solve for t

We want to isolate t.

- Subtract V from both sides:

> v - V = gt

- Divide both sides by g:

> t = (v - V)/g

✔ Final Answer: t = (v - V)/g

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11. S = P + prt; solve for r

We want to isolate r.

- Subtract P from both sides:

> S - P = prt

- Divide both sides by pt:

> r = (S - P)/(pt)

✔ Final Answer: r = (S - P)/(pt)

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12. A = (1/2)h(b + c); solve for c

We want to isolate c.

- Multiply both sides by 2:

> 2A = h(b + c)

- Divide both sides by h:

> 2A/h = b + c

- Subtract b from both sides:

> c = (2A/h) - b

✔ Final Answer: c = (2A/h) - b

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13. F = (9/5)C + 32; solve for C

This is the Fahrenheit to Celsius formula — we’re solving for C.

- Subtract 32 from both sides:

> F - 32 = (9/5)C

- Multiply both sides by 5/9:

> C = (5/9)(F - 32)

✔ Final Answer: C = (5/9)(F - 32)

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14. (am - bn)/c = d; solve for m

We want to isolate m.

- Multiply both sides by c:

> am - bn = cd

- Add bn to both sides:

> am = cd + bn

- Divide both sides by a:

> m = (cd + bn)/a

✔ Final Answer: m = (cd + bn)/a

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## ✔ All Answers Summarized:

1. B = V/h
2. c = dr
3. W = A/L
4. w = 2x / r²
5. h = 3V / b²
6. E₁ = (Fd²)/(kE₂)
7. z = 6w + 10
8. b = (5ax - cx + c)/2
9. x = (b - a)/3
10. t = (v - V)/g
11. r = (S - P)/(pt)
12. c = (2A/h) - b
13. C = (5/9)(F - 32)
14. m = (cd + bn)/a

Let me know if you’d like to see any step explained in more detail!