Use this guided notes sheet to introduce students to literal equations, featuring key definitions and step-by-step practice problems.

Let's solve each of the literal equation problems step by step and fill in the blanks at the top.

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Definitions:

- Literal equation – an equation with multiple variables
*(These are equations that involve more than one variable, often used in formulas.)*

- Literal equations are useful when using formulas.
*(For example, solving for one variable in a formula like $ V = \frac{d}{t} $ allows you to find distance, time, or velocity depending on what’s known.)*

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Now let's solve each problem:

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1. Solve the equation for $ m $.

$$
\frac{m}{n} = o
$$

Step 1: Multiply both sides by $ n $ to eliminate the denominator:
$$
m = o \cdot n
$$

✔ Answer: $ m = on $

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2. Isolate $ j $.

$$
j - k = h
$$

Step 1: Add $ k $ to both sides:
$$
j = h + k
$$

✔ Answer: $ j = h + k $

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3. Find the expression that represents the value of $ p $.

$$
pr = t
$$

Step 1: Divide both sides by $ r $:
$$
p = \frac{t}{r}
$$

✔ Answer: $ p = \frac{t}{r} $

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4. Solve for $ x $.

$$
ax - 5 = 10
$$

Step 1: Add 5 to both sides:
$$
ax = 15
$$

Step 2: Divide both sides by $ a $:
$$
x = \frac{15}{a}
$$

✔ Answer: $ x = \frac{15}{a} $

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5. Solve the equation for $ g $.

$$
3(g - h) = 14
$$

Step 1: Divide both sides by 3:
$$
g - h = \frac{14}{3}
$$

Step 2: Add $ h $ to both sides:
$$
g = \frac{14}{3} + h
$$

✔ Answer: $ g = h + \frac{14}{3} $ or $ g = \frac{14}{3} + h $

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6. Find the expression that represents the value of $ e $.

$$
5e - 8 = 2e + f
$$

Step 1: Subtract $ 2e $ from both sides:
$$
3e - 8 = f
$$

Step 2: Add 8 to both sides:
$$
3e = f + 8
$$

Step 3: Divide both sides by 3:
$$
e = \frac{f + 8}{3}
$$

✔ Answer: $ e = \frac{f + 8}{3} $

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✔ Final Answers:

1. $ m = on $
2. $ j = h + k $
3. $ p = \frac{t}{r} $
4. $ x = \frac{15}{a} $
5. $ g = h + \frac{14}{3} $
6. $ e = \frac{f + 8}{3} $

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📝 Summary:

- A literal equation is an equation with multiple variables.
- They are useful when using formulas (like physics, geometry, etc.).

This worksheet helps students practice manipulating formulas to solve for different variables — a key skill in algebra and science!