https://file.aiquickdraw.com/mathbot/file/1727916167317nff18zgl.jpg

Let's work through the equations on this worksheet step by step. The goal is to solve for the specified variable in each case. Here are the solutions:

### Rewrite each equation to solve for **m**:

1. **\( m + 3n = 7 \)**  
   \[
   m = 7 - 3n
   \]

2. **\( -3m - 9n = 24 \)**  
   \[
   -3m = 24 + 9n \quad \text{(add \(9n\) to both sides)}  
   m = \frac{24 + 9n}{-3} = -8 - 3n
   \]

3. **\( -5n = 4m + 8 \)**  
   \[
   4m = -5n - 8 \quad \text{(subtract 8 from both sides)}  
   m = \frac{-5n - 8}{4}
   \]

4. **\( 2m = -6n - 5 \)**  
   \[
   m = \frac{-6n - 5}{2}
   \]

5. **\( 8n = -3m + 1 \)**  
   \[
   -3m = 8n - 1 \quad \text{(subtract 1 from both sides)}  
   m = \frac{8n - 1}{-3}
   \]

6. **\( 4n - 6m = -2 \)**  
   \[
   -6m = -4n - 2 \quad \text{(subtract \(4n\) from both sides)}  
   m = \frac{-4n - 2}{-6} = \frac{2n + 1}{3}
   \]

7. **\( -5n = 13 - 3m \)**  
   \[
   3m = 13 + 5n \quad \text{(add \(5n\) to both sides)}  
   m = \frac{13 + 5n}{3}
   \]

8. **\( 10m + 6n = 12 \)**  
   \[
   10m = 12 - 6n \quad \text{(subtract \(6n\) from both sides)}  
   m = \frac{12 - 6n}{10} = \frac{6 - 3n}{5}
   \]

### Rewrite each equation to solve for **x**:

9. **\( y = 3x + 5 \)**  
   \[
   3x = y - 5  
   x = \frac{y - 5}{3}
   \]

10. **\( qx + x = r \)**  
    \[
    x(q + 1) = r  
    x = \frac{r}{q + 1}
    \]

11. **\( m = \frac{x + n}{p} \)**  
    \[
    x + n = mp  
    x = mp - n
    \]

12. **\( d = f + fx \)**  
    \[
    d = f(1 + x)  
    x = \frac{d}{f} - 1
    \]

13. **\( -3(x + n) = x \)**  
    \[
    -3x - 3n = x  
    -4x = 3n  
    x = -\frac{3n}{4}
    \]

14. **\( \frac{x - 4}{y + 2} = 5 \)**  
    \[
    x - 4 = 5(y + 2)  
    x = 5(y + 2) + 4 = 5y + 10 + 4 = 5y + 14
    \]

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Would you like any further details on a specific problem or step?

### Follow-up Questions:
1. What is the general process for solving literal equations?
2. How can you handle equations with fractions when solving for a variable?
3. Can you provide an example of solving an equation with multiple variables on both sides?
4. What strategies can you use if the variable appears in multiple terms?
5. How does distributing terms in parentheses affect solving an equation?

**Tip:** When solving literal equations, always aim to isolate the variable step by step, performing the same operations on both sides of the equation.

Solve the given equations by isolating the specified variable. The equations include solving for 'm' and 'x' in various linear equations.

Step-by-step solutions for solving linear equations to isolate variables 'm' and 'x'. Learn how to apply algebraic concepts, the distributive property, and properties of equality to solve equations such as 'm + 3n = 7' and 'y = 3x + 5'. Suitable for Grades 7-9.

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