Ced. 4 Literal Equations Worksheet 20 More Problems | PDF ... - Free Printable

Let's solve each of these literal equations for the indicated variable. We'll go step by step, showing the algebraic manipulations needed to isolate the desired variable.

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1. $ P = IRT $  for $ T $

We want to solve for $ T $.
Divide both sides by $ IR $:

$$
T = \frac{P}{IR}
$$

✔ Answer: $ T = \frac{P}{IR} $

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2. $ A = 2L + W $  for $ W $

We want to solve for $ W $.
Subtract $ 2L $ from both sides:

$$
W = A - 2L
$$

✔ Answer: $ W = A - 2L $

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3. $ y = 5x - 6 $  for $ x $

We want to solve for $ x $.
Add 6 to both sides:

$$
y + 6 = 5x
$$

Now divide by 5:

$$
x = \frac{y + 6}{5}
$$

✔ Answer: $ x = \frac{y + 6}{5} $

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4. $ 2x - 3y = 8 $  for $ y $

We want to solve for $ y $.
Subtract $ 2x $ from both sides:

$$
-3y = 8 - 2x
$$

Divide both sides by $ -3 $:

$$
y = \frac{2x - 8}{3}
$$

(Note: $ \frac{8 - 2x}{-3} = \frac{2x - 8}{3} $)

✔ Answer: $ y = \frac{2x - 8}{3} $

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5. $ \frac{x + y}{3} = 5 $  for $ x $

Multiply both sides by 3:

$$
x + y = 15
$$

Subtract $ y $ from both sides:

$$
x = 15 - y
$$

✔ Answer: $ x = 15 - y $

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6. $ y = mx + b $  for $ b $

We want to solve for $ b $.
Subtract $ mx $ from both sides:

$$
b = y - mx
$$

✔ Answer: $ b = y - mx $

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7. $ ax + by = c $  for $ y $

We want to solve for $ y $.
Subtract $ ax $ from both sides:

$$
by = c - ax
$$

Divide both sides by $ b $:

$$
y = \frac{c - ax}{b}
$$

✔ Answer: $ y = \frac{c - ax}{b} $

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8. $ A = \frac{1}{2} h b + c $  for $ b $

We want to solve for $ b $.
First, subtract $ c $ from both sides:

$$
A - c = \frac{1}{2} h b
$$

Now multiply both sides by 2:

$$
2(A - c) = h b
$$

Divide both sides by $ h $:

$$
b = \frac{2(A - c)}{h}
$$

✔ Answer: $ b = \frac{2(A - c)}{h} $

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9. $ V = LWH $  for $ L $

We want to solve for $ L $.
Divide both sides by $ WH $:

$$
L = \frac{V}{WH}
$$

✔ Answer: $ L = \frac{V}{WH} $

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10. $ W = 4\pi r $  for $ r $

We want to solve for $ r $.
Divide both sides by $ 4\pi $:

$$
r = \frac{W}{4\pi}
$$

✔ Answer: $ r = \frac{W}{4\pi} $

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11. $ V = \pi r^2 h $  for $ h $

We want to solve for $ h $.
Divide both sides by $ \pi r^2 $:

$$
h = \frac{V}{\pi r^2}
$$

✔ Answer: $ h = \frac{V}{\pi r^2} $

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12. $ 7x - y = 14 $  for $ x $

We want to solve for $ x $.
Add $ y $ to both sides:

$$
7x = 14 + y
$$

Divide both sides by 7:

$$
x = \frac{14 + y}{7}
$$

This can also be written as:

$$
x = 2 + \frac{y}{7}
$$

✔ Answer: $ x = \frac{14 + y}{7} $ or $ x = 2 + \frac{y}{7} $

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✔ Final Answers Summary:

1. $ T = \frac{P}{IR} $
2. $ W = A - 2L $
3. $ x = \frac{y + 6}{5} $
4. $ y = \frac{2x - 8}{3} $
5. $ x = 15 - y $
6. $ b = y - mx $
7. $ y = \frac{c - ax}{b} $
8. $ b = \frac{2(A - c)}{h} $
9. $ L = \frac{V}{WH} $
10. $ r = \frac{W}{4\pi} $
11. $ h = \frac{V}{\pi r^2} $
12. $ x = \frac{14 + y}{7} $

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