Math worksheet for simplifying linear expressions by adding and subtracting.

Let's solve each of these problems step by step. The goal is to simplify each linear expression by combining like terms. We'll handle the operations (addition and subtraction) carefully, especially with signs.

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

Distribute the negative sign to the second expression:
$$
-6p - 8 - 2p + 6
$$
Combine like terms:
$$
(-6p - 2p) + (-8 + 6) = -8p - 2
$$
✔ Answer: $-8p - 2$

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

Remove parentheses and combine:
$$
-8r - 2 + 4r - 3
$$
Combine like terms:
$$
(-8r + 4r) + (-2 - 3) = -4r - 5
$$
✔ Answer: $-4r - 5$

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

Distribute the negative:
$$
-z - 8 - 6z + 5
$$
Combine:
$$
(-z - 6z) + (-8 + 5) = -7z - 3
$$
✔ Answer: $-7z - 3$

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

Remove parentheses:
$$
-s - 5 - 2s + 2
$$
Combine:
$$
(-s - 2s) + (-5 + 2) = -3s - 3
$$
✔ Answer: $-3s - 3$

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

Distribute the negative:
$$
-7s + 4 + 8s - 4
$$
Combine:
$$
(-7s + 8s) + (4 - 4) = s + 0 = s
$$
✔ Answer: $s$

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

Distribute the negative:
$$
-4f + 9 - 8f - 9
$$
Combine:
$$
(-4f - 8f) + (9 - 9) = -12f + 0 = -12f
$$
✔ Answer: $-12f$

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

Remove parentheses:
$$
-8f - f + 8
$$
Combine:
$$
(-8f - f) + 8 = -9f + 8
$$
✔ Answer: $-9f + 8$

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

Remove parentheses:
$$
4p - 4 - 7p - 7
$$
Combine:
$$
(4p - 7p) + (-4 - 7) = -3p - 11
$$
✔ Answer: $-3p - 11$

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

Distribute the negative:
$$
7v - 9 - 6v - 9
$$
Combine:
$$
(7v - 6v) + (-9 - 9) = v - 18
$$
✔ Answer: $v - 18$

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

Remove parentheses:
$$
-3g + 5g - 5
$$
Combine:
$$
(-3g + 5g) - 5 = 2g - 5
$$
✔ Answer: $2g - 5$

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✔ Final Answers:

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

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🔍 Summary of Key Steps:

- Distribute negatives when subtracting expressions.
- Combine like terms: variables with same letter and constants separately.
- Always watch the signs, especially double negatives.

Let me know if you'd like a printable version or further explanation!