Simplify algebraic expressions by combining like terms.

Let's solve each expression by collecting like terms. Like terms are terms that have the same variable(s) raised to the same power. We combine them by adding or subtracting their coefficients.

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a) $ 2x + 6y + 7x $

- Like terms: $2x$ and $7x$
- Combine: $2x + 7x = 9x$
- $6y$ has no like term

✔ Answer: $9x + 6y$

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b) $ 3a + 8b + 5a $

- Like terms: $3a$ and $5a$
- Combine: $3a + 5a = 8a$
- $8b$ has no like term

✔ Answer: $8a + 8b$

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c) $ 6u + 3v - 2u $

- Like terms: $6u$ and $-2u$
- Combine: $6u - 2u = 4u$
- $3v$ has no like term

✔ Answer: $4u + 3v$

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d) $ 9p + 8q - p $

- Like terms: $9p$ and $-p$
- Combine: $9p - p = 8p$
- $8q$ has no like term

✔ Answer: $8p + 8q$

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e) $ 2m + 5n + 4m + 3n $

- Like terms:
- $2m$ and $4m$: $2m + 4m = 6m$
- $5n$ and $3n$: $5n + 3n = 8n$

✔ Answer: $6m + 8n$

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f) $ 6u + 9v + u + 3v $

- Like terms:
- $6u$ and $u$: $6u + u = 7u$
- $9v$ and $3v$: $9v + 3v = 12v$

✔ Answer: $7u + 12v$

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g) $ 8b + 7c + 3b - 2c $

- Like terms:
- $8b$ and $3b$: $8b + 3b = 11b$
- $7c$ and $-2c$: $7c - 2c = 5c$

✔ Answer: $11b + 5c$

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h) $ a + 2b + a - b $

- Like terms:
- $a$ and $a$: $a + a = 2a$
- $2b$ and $-b$: $2b - b = b$

✔ Answer: $2a + b$

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i) $ 5a + 2b - 5a + 6b $

- Like terms:
- $5a$ and $-5a$: $5a - 5a = 0$ (they cancel out)
- $2b$ and $6b$: $2b + 6b = 8b$

✔ Answer: $8b$

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j) $ 9p + 3q - 2p - 3q $

- Like terms:
- $9p$ and $-2p$: $9p - 2p = 7p$
- $3q$ and $-3q$: $3q - 3q = 0$ (they cancel out)

✔ Answer: $7p$

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✔ Final Answers:

a) $9x + 6y$
b) $8a + 8b$
c) $4u + 3v$
d) $8p + 8q$
e) $6m + 8n$
f) $7u + 12v$
g) $11b + 5c$
h) $2a + b$
i) $8b$
j) $7p$

Let me know if you'd like these written in a different format!