Adding and Subtracting and Simplifying Linear Expressions (A) - Free Printable

Problem: Simplify each linear expression.

We are tasked with simplifying the given expressions by combining like terms. Let's solve each problem step by step.

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#### 1. $(-6p - 8) - (2p - 6)$

1. Distribute the negative sign through the second parenthesis:
$$
-6p - 8 - 2p + 6
$$

2. Combine like terms:
- For the $p$-terms: $-6p - 2p = -8p$
- For the constant terms: $-8 + 6 = -2$

3. Write the simplified expression:
$$
-8p - 2
$$

Answer: $\boxed{-8p - 2}$

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#### 2. $(-8r - 2) + (4r - 3)$

1. Remove the parentheses (no distribution needed since there is a plus sign):
$$
-8r - 2 + 4r - 3
$$

2. Combine like terms:
- For the $r$-terms: $-8r + 4r = -4r$
- For the constant terms: $-2 - 3 = -5$

3. Write the simplified expression:
$$
-4r - 5
$$

Answer: $\boxed{-4r - 5}$

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#### 3. $(-z - 8) - (6z - 5)$

1. Distribute the negative sign through the second parenthesis:
$$
-z - 8 - 6z + 5
$$

2. Combine like terms:
- For the $z$-terms: $-z - 6z = -7z$
- For the constant terms: $-8 + 5 = -3$

3. Write the simplified expression:
$$
-7z - 3
$$

Answer: $\boxed{-7z - 3}$

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#### 4. $(-s - 5) + (-2s + 2)$

1. Remove the parentheses (no distribution needed since there is a plus sign):
$$
-s - 5 - 2s + 2
$$

2. Combine like terms:
- For the $s$-terms: $-s - 2s = -3s$
- For the constant terms: $-5 + 2 = -3$

3. Write the simplified expression:
$$
-3s - 3
$$

Answer: $\boxed{-3s - 3}$

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#### 5. $(-7s + 4) - (-8s + 4)$

1. Distribute the negative sign through the second parenthesis:
$$
-7s + 4 + 8s - 4
$$

2. Combine like terms:
- For the $s$-terms: $-7s + 8s = s$
- For the constant terms: $4 - 4 = 0$

3. Write the simplified expression:
$$
s
$$

Answer: $\boxed{s}$

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#### 6. $(-4f + 9) - (8f + 9)$

1. Distribute the negative sign through the second parenthesis:
$$
-4f + 9 - 8f - 9
$$

2. Combine like terms:
- For the $f$-terms: $-4f - 8f = -12f$
- For the constant terms: $9 - 9 = 0$

3. Write the simplified expression:
$$
-12f
$$

Answer: $\boxed{-12f}$

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#### 7. $(-8f) + (-f + 8)$

1. Remove the parentheses (no distribution needed since there is a plus sign):
$$
-8f - f + 8
$$

2. Combine like terms:
- For the $f$-terms: $-8f - f = -9f$
- For the constant terms: $8$ (remains as is)

3. Write the simplified expression:
$$
-9f + 8
$$

Answer: $\boxed{-9f + 8}$

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#### 8. $(4p - 4) + (-7p - 7)$

1. Remove the parentheses (no distribution needed since there is a plus sign):
$$
4p - 4 - 7p - 7
$$

2. Combine like terms:
- For the $p$-terms: $4p - 7p = -3p$
- For the constant terms: $-4 - 7 = -11$

3. Write the simplified expression:
$$
-3p - 11
$$

Answer: $\boxed{-3p - 11}$

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#### 9. $(7v - 9) - (6v + 9)$

1. Distribute the negative sign through the second parenthesis:
$$
7v - 9 - 6v - 9
$$

2. Combine like terms:
- For the $v$-terms: $7v - 6v = v$
- For the constant terms: $-9 - 9 = -18$

3. Write the simplified expression:
$$
v - 18
$$

Answer: $\boxed{v - 18}$

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#### 10. $(-3g) + (5g + 5)$

1. Remove the parentheses (no distribution needed since there is a plus sign):
$$
-3g + 5g + 5
$$

2. Combine like terms:
- For the $g$-terms: $-3g + 5g = 2g$
- For the constant terms: $5$ (remains as is)

3. Write the simplified expression:
$$
2g + 5
$$

Answer: $\boxed{2g + 5}$

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Final Answers:

1. $\boxed{-8p - 2}$
2. $\boxed{-4r - 5}$
3. $\boxed{-7z - 3}$
4. $\boxed{-3s - 3}$
5. $\boxed{s}$
6. $\boxed{-12f}$
7. $\boxed{-9f + 8}$
8. $\boxed{-3p - 11}$
9. $\boxed{v - 18}$
10. $\boxed{2g + 5}$

$\boxed{\text{Final Answers: } -8p - 2, -4r - 5, -7z - 3, -3s - 3, s, -12f, -9f + 8, -3p - 11, v - 18, 2g + 5}$