This worksheet helps students master the skill of simplifying algebraic expressions by combining like terms and using the distributive property.

To solve the problem of combining like terms, we need to simplify each expression by grouping and adding or subtracting terms that have the same variable. Let's go through each expression step by step.

---

Problem #1:

\[
-7 + 13x + 2x + 8
\]

1. Identify the like terms:
- Constant terms: \(-7\) and \(8\)
- \(x\)-terms: \(13x\) and \(2x\)

2. Combine the constant terms:
\[
-7 + 8 = 1
\]

3. Combine the \(x\)-terms:
\[
13x + 2x = 15x
\]

4. Write the simplified expression:
\[
15x + 1
\]

Answer:
\[
\boxed{15x + 1}
\]

---

Problem #2:

\[
9 + 7y - 2 - 5y
\]

1. Identify the like terms:
- Constant terms: \(9\) and \(-2\)
- \(y\)-terms: \(7y\) and \(-5y\)

2. Combine the constant terms:
\[
9 - 2 = 7
\]

3. Combine the \(y\)-terms:
\[
7y - 5y = 2y
\]

4. Write the simplified expression:
\[
2y + 7
\]

Answer:
\[
\boxed{2y + 7}
\]

---

Problem #3:

\[
2 + 3x - 4x + 6
\]

1. Identify the like terms:
- Constant terms: \(2\) and \(6\)
- \(x\)-terms: \(3x\) and \(-4x\)

2. Combine the constant terms:
\[
2 + 6 = 8
\]

3. Combine the \(x\)-terms:
\[
3x - 4x = -x
\]

4. Write the simplified expression:
\[
-x + 8
\]

Answer:
\[
\boxed{-x + 8}
\]

---

Problem #4:

\[
5 + 2x + 2
\]

1. Identify the like terms:
- Constant terms: \(5\) and \(2\)
- \(x\)-terms: \(2x\)

2. Combine the constant terms:
\[
5 + 2 = 7
\]

3. The \(x\)-term remains as it is:
\[
2x
\]

4. Write the simplified expression:
\[
2x + 7
\]

Answer:
\[
\boxed{2x + 7}
\]

---

Problem #5:

\[
2(4x - 1) + x
\]

1. Distribute the \(2\) across the terms inside the parentheses:
\[
2 \cdot 4x - 2 \cdot 1 = 8x - 2
\]

2. Add the remaining term \(x\):
\[
8x - 2 + x
\]

3. Identify the like terms:
- Constant terms: \(-2\)
- \(x\)-terms: \(8x\) and \(x\)

4. Combine the \(x\)-terms:
\[
8x + x = 9x
\]

5. Write the simplified expression:
\[
9x - 2
\]

Answer:
\[
\boxed{9x - 2}
\]

---

Problem #6:

\[
6x + 2(x + 4)
\]

1. Distribute the \(2\) across the terms inside the parentheses:
\[
2 \cdot x + 2 \cdot 4 = 2x + 8
\]

2. Add the remaining term \(6x\):
\[
6x + 2x + 8
\]

3. Identify the like terms:
- Constant terms: \(8\)
- \(x\)-terms: \(6x\) and \(2x\)

4. Combine the \(x\)-terms:
\[
6x + 2x = 8x
\]

5. Write the simplified expression:
\[
8x + 8
\]

Answer:
\[
\boxed{8x + 8}
\]

---

Problem #7:

\[
3(x + 5) - 10
\]

1. Distribute the \(3\) across the terms inside the parentheses:
\[
3 \cdot x + 3 \cdot 5 = 3x + 15
\]

2. Subtract \(10\):
\[
3x + 15 - 10
\]

3. Identify the like terms:
- Constant terms: \(15\) and \(-10\)
- \(x\)-terms: \(3x\)

4. Combine the constant terms:
\[
15 - 10 = 5
\]

5. Write the simplified expression:
\[
3x + 5
\]

Answer:
\[
\boxed{3x + 5}
\]

---

Problem #8:

\[
15x - (x - 4)
\]

1. Distribute the negative sign across the terms inside the parentheses:
\[
15x - x + 4
\]

2. Identify the like terms:
- Constant terms: \(4\)
- \(x\)-terms: \(15x\) and \(-x\)

3. Combine the \(x\)-terms:
\[
15x - x = 14x
\]

4. Write the simplified expression:
\[
14x + 4
\]

Answer:
\[
\boxed{14x + 4}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
&1. \, 15x + 1 \\
&2. \, 2y + 7 \\
&3. \, -x + 8 \\
&4. \, 2x + 7 \\
&5. \, 9x - 2 \\
&6. \, 8x + 8 \\
&7. \, 3x + 5 \\
&8. \, 14x + 4
\end{aligned}
}
\]