This worksheet provides eight practice problems for students to solve literal equations by isolating specific variables.

Here's the step-by-step solution for each of the 8 literal equations, solving for the specified variable.

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1. Solve for \( b \):
\[ a + \frac{b}{c} = d \]

Step 1: Subtract \( a \) from both sides to isolate the term with \( b \):
\[ \frac{b}{c} = d - a \]

Step 2: Multiply both sides by \( c \) to solve for \( b \):
\[ b = c(d - a) \]

✔ Final Answer: \( \boxed{b = c(d - a)} \)

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2. Isolate the variable \( x \):
\[ 3 - x + k = 12 \]

Step 1: Combine constants on the left (optional, but helpful):
We can rearrange:
\[ -x + (3 + k) = 12 \]

Step 2: Subtract \( (3 + k) \) from both sides:
\[ -x = 12 - 3 - k \]
\[ -x = 9 - k \]

Step 3: Multiply both sides by -1 to solve for \( x \):
\[ x = -9 + k \quad \text{or} \quad x = k - 9 \]

✔ Final Answer: \( \boxed{x = k - 9} \)

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3. Solve for \( y \):
\[ \frac{1}{2}(2y - 6n) = 5n \]

Step 1: Distribute the \( \frac{1}{2} \):
\[ \frac{1}{2} \cdot 2y - \frac{1}{2} \cdot 6n = 5n \]
\[ y - 3n = 5n \]

Step 2: Add \( 3n \) to both sides:
\[ y = 5n + 3n \]
\[ y = 8n \]

✔ Final Answer: \( \boxed{y = 8n} \)

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4. Solve the equation for \( w \):
\[ w + 2 = e - 4 \]

Step 1: Subtract 2 from both sides:
\[ w = e - 4 - 2 \]
\[ w = e - 6 \]

✔ Final Answer: \( \boxed{w = e - 6} \)

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5. Find the expression that represents the value of \( v \):
\[ 2(v - 8) = n + y \]

Step 1: Divide both sides by 2:
\[ v - 8 = \frac{n + y}{2} \]

Step 2: Add 8 to both sides:
\[ v = \frac{n + y}{2} + 8 \]

You can also write this as a single fraction:
\[ v = \frac{n + y + 16}{2} \]

✔ Final Answer: \( \boxed{v = \frac{n + y}{2} + 8} \) or \( \boxed{v = \frac{n + y + 16}{2}} \)

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6. Isolate the variable \( r \):
\[ rs - 5 = t \]

Step 1: Add 5 to both sides:
\[ rs = t + 5 \]

Step 2: Divide both sides by \( s \) (assuming \( s \ne 0 \)):
\[ r = \frac{t + 5}{s} \]

✔ Final Answer: \( \boxed{r = \frac{t + 5}{s}} \)

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7. Solve the equation for \( a \):
\[ t - ga = u \]

Step 1: Subtract \( t \) from both sides:
\[ -ga = u - t \]

Step 2: Divide both sides by \( -g \) (assuming \( g \ne 0 \)):
\[ a = \frac{u - t}{-g} = \frac{t - u}{g} \]

✔ Final Answer: \( \boxed{a = \frac{t - u}{g}} \)

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8. Solve for \( b \):
\[ \frac{b - 5}{c} = k \]

Step 1: Multiply both sides by \( c \) (assuming \( c \ne 0 \)):
\[ b - 5 = kc \]

Step 2: Add 5 to both sides:
\[ b = kc + 5 \]

✔ Final Answer: \( \boxed{b = kc + 5} \)

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✔ Summary of All Answers:

1. \( b = c(d - a) \)
2. \( x = k - 9 \)
3. \( y = 8n \)
4. \( w = e - 6 \)
5. \( v = \frac{n + y}{2} + 8 \)
6. \( r = \frac{t + 5}{s} \)
7. \( a = \frac{t - u}{g} \)
8. \( b = kc + 5 \)

Let me know if you’d like these explained in more detail or want to check your work!