Let's solve each of these linear expression problems step by step. The goal is to
simplify each expression by combining like terms. Remember:
- When
adding expressions, you can combine like terms directly.
- When
subtracting expressions, distribute the negative sign to every term inside the parentheses before combining.
---
1. $(-6p - 8) - (2p - 6)$
Distribute the negative sign:
$$
-6p - 8 - 2p + 6
$$
Combine like terms:
$$
(-6p - 2p) + (-8 + 6) = -8p - 2
$$
✔ Answer: $-8p - 2$
---
2. $(-8r - 2) + (4r - 3)$
Remove parentheses and combine:
$$
-8r - 2 + 4r - 3 = (-8r + 4r) + (-2 - 3) = -4r - 5
$$
✔ Answer: $-4r - 5$
---
3. $(-z - 8) - (6z - 5)$
Distribute the negative:
$$
-z - 8 - 6z + 5 = (-z - 6z) + (-8 + 5) = -7z - 3
$$
✔ Answer: $-7z - 3$
---
4. $(-s - 5) + (-2s + 2)$
Combine:
$$
-s - 5 - 2s + 2 = (-s - 2s) + (-5 + 2) = -3s - 3
$$
✔ Answer: $-3s - 3$
---
5. $(-7s + 4) - (-8s + 4)$
Distribute the negative:
$$
-7s + 4 + 8s - 4 = (-7s + 8s) + (4 - 4) = s + 0 = s
$$
✔ Answer: $s$
---
6. $(-4f + 9) - (8f + 9)$
Distribute the negative:
$$
-4f + 9 - 8f - 9 = (-4f - 8f) + (9 - 9) = -12f + 0 = -12f
$$
✔ Answer: $-12f$
---
7. $(-8f) + (-f + 8)$
Rewrite: $-8f - f + 8 = (-8f - f) + 8 = -9f + 8$
✔ Answer: $-9f + 8$
---
8. $(4p - 4) + (-7p - 7)$
Combine:
$$
4p - 4 - 7p - 7 = (4p - 7p) + (-4 - 7) = -3p - 11
$$
✔ Answer: $-3p - 11$
---
9. $(7v - 9) - (6v + 9)$
Distribute the negative:
$$
7v - 9 - 6v - 9 = (7v - 6v) + (-9 - 9) = v - 18
$$
✔ Answer: $v - 18$
---
10. $(-3g) + (5g - 5)$
Combine:
$$
-3g + 5g - 5 = ( -3g + 5g ) - 5 = 2g - 5
$$
✔ Answer: $2g - 5$
---
✔ 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. $2g - 5$
Let me know if you'd like a printable version or explanation in another format!
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting algebraic expressions worksheet.
