Algebra 1 homework assignment focusing on simplifying expressions by combining like terms, with problems numbered 1 to 12.

Let's solve each expression step by step by combining like terms and simplifying. We'll go through each problem one at a time.

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1) $-16n - 14n$

These are like terms (both have $n$).

$$
-16n - 14n = (-16 - 14)n = -30n
$$

✔ Answer: $-30n$

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2) $15n - 19n$

Like terms again:

$$
15n - 19n = (15 - 19)n = -4n
$$

✔ Answer: $-4n$

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3) $-4 + 7(1 - 3m)$

First, distribute the 7:

$$
7(1 - 3m) = 7 \cdot 1 - 7 \cdot 3m = 7 - 21m
$$

Now add the $-4$:

$$
-4 + 7 - 21m = 3 - 21m
$$

✔ Answer: $3 - 21m$

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4) $-5n + 3(6 + 7n)$

Distribute the 3:

$$
3(6 + 7n) = 18 + 21n
$$

Now combine with $-5n$:

$$
-5n + 18 + 21n = (-5n + 21n) + 18 = 16n + 18
$$

✔ Answer: $16n + 18$

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5) $-2n - (9 - 10n)$

Distribute the negative sign across the parentheses:

$$
-2n - 9 + 10n
$$

Now combine like terms:

$$
(-2n + 10n) - 9 = 8n - 9
$$

✔ Answer: $8n - 9$

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6) $10 - 5(9n - 9)$

Distribute the $-5$:

$$
-5(9n - 9) = -45n + 45
$$

Now add to 10:

$$
10 - 45n + 45 = (-45n) + (10 + 45) = -45n + 55
$$

✔ Answer: $-45n + 55$

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7) $9a + 10(6a - 1)$

Distribute the 10:

$$
10(6a - 1) = 60a - 10
$$

Now add $9a$:

$$
9a + 60a - 10 = 69a - 10
$$

✔ Answer: $69a - 10$

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8) $-9(6m - 3) + 6(1 + 4m)$

Distribute both:

- $-9(6m - 3) = -54m + 27$
- $6(1 + 4m) = 6 + 24m$

Now combine all:

$$
-54m + 27 + 6 + 24m = (-54m + 24m) + (27 + 6) = -30m + 33
$$

✔ Answer: $-30m + 33$

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9) $-10(1 - 9x) + 6(x - 10)$

Distribute:

- $-10(1 - 9x) = -10 + 90x$
- $6(x - 10) = 6x - 60$

Now combine:

$$
-10 + 90x + 6x - 60 = (90x + 6x) + (-10 - 60) = 96x - 70
$$

✔ Answer: $96x - 70$

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10) $5(-2n + 4) + 2(n + 3)$

Distribute:

- $5(-2n + 4) = -10n + 20$
- $2(n + 3) = 2n + 6$

Now combine:

$$
-10n + 20 + 2n + 6 = (-10n + 2n) + (20 + 6) = -8n + 26
$$

✔ Answer: $-8n + 26$

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11) $-3(10b + 10) + 5(b + 2)$

Distribute:

- $-3(10b + 10) = -30b - 30$
- $5(b + 2) = 5b + 10$

Now combine:

$$
-30b - 30 + 5b + 10 = (-30b + 5b) + (-30 + 10) = -25b - 20
$$

✔ Answer: $-25b - 20$

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12) $-7(n + 3) - 8(1 + 8n)$

Distribute:

- $-7(n + 3) = -7n - 21$
- $-8(1 + 8n) = -8 - 64n$

Now combine:

$$
-7n - 21 - 8 - 64n = (-7n - 64n) + (-21 - 8) = -71n - 29
$$

✔ Answer: $-71n - 29$

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✔ Final Answers:

1) $-30n$
2) $-4n$
3) $3 - 21m$
4) $16n + 18$
5) $8n - 9$
6) $-45n + 55$
7) $69a - 10$
8) $-30m + 33$
9) $96x - 70$
10) $-8n + 26$
11) $-25b - 20$
12) $-71n - 29$

Let me know if you'd like these written in a formatted worksheet style!