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Let's go through the math problems step by step. Here are the answers and explanations for each problem on the worksheet:

### 1. \( y - 17 = -37 \)
To solve for \( y \):
\[
y - 17 = -37 \\
y = -37 + 17 = -20
\]
Answer: \( y = -20 \)

### 2. \( -12 + k = 18 \)
To solve for \( k \):
\[
-12 + k = 18 \\
k = 18 + 12 = 30
\]
Answer: \( k = 30 \)

### 3. \( 5m = -20 \)
To solve for \( m \):
\[
5m = -20 \\
m = \frac{-20}{5} = -4
\]
Answer: \( m = -4 \)

### 4. \( \frac{x}{9} = 27 \)
To solve for \( x \):
\[
\frac{x}{9} = 27 \\
x = 27 \times 9 = 243
\]
Answer: \( x = 243 \)

### 5. \( \frac{4}{5} z = 16 \)
To solve for \( z \):
\[
\frac{4}{5} z = 16 \\
z = 16 \times \frac{5}{4} = 16 \times 1.25 = 20
\]
Answer: \( z = 20 \)

### 6. \( 3p - 4 = 11 \)
To solve for \( p \):
\[
3p - 4 = 11 \\
3p = 11 + 4 = 15 \\
p = \frac{15}{3} = 5
\]
Answer: \( p = 5 \)

### 7. \( -5a + 7 = -38 \)
To solve for \( a \):
\[
-5a + 7 = -38 \\
-5a = -38 - 7 = -45 \\
a = \frac{-45}{-5} = 9
\]
Answer: \( a = 9 \)

### 8. \( 31 - 12n = 211 \)
To solve for \( n \):
\[
31 - 12n = 211 \\
-12n = 211 - 31 = 180 \\
n = \frac{180}{-12} = -15
\]
Answer: \( n = -15 \)

### 9. \( \frac{x}{3} = 15 \)
To solve for \( x \):
\[
\frac{x}{3} = 15 \\
x = 15 \times 3 = 45
\]
Answer: \( x = 45 \)

Let me know if you want the remaining questions to be solved! Would you like a deeper explanation for any specific problem or more details?

Here are some additional questions related to solving linear equations:
1. What is the general strategy for solving equations that involve fractions?
2. How do you solve a two-step equation with both addition and division?
3. Why is it important to reverse the order of operations when solving equations?
4. How can you check if your solution to a linear equation is correct?
5. What happens if an equation has no solution or an infinite number of solutions?

**Tip:** Always isolate the variable by performing inverse operations step by step (reverse order of operations).

This worksheet focuses on solving one-step and two-step equations, including equations with fractions. Topics covered include basic algebraic manipulation, inverse operations, and fraction equations. Suitable for students in grades 6-8.

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