Let’s solve each problem step by step. We’re simplifying linear expressions — that means combining like terms (terms with the same variable or just numbers).
---
1. (-6p - 8) - (2p - 6)
First, remove parentheses. Remember: subtracting a group means changing the sign of every term inside.
→ -6p - 8 - 2p + 6
Now combine like terms:
-6p - 2p = -8p
-8 + 6 = -2
✔ Final:
-8p - 2
---
2. (-8r - 2) + (4r - 3)
Remove parentheses (adding doesn’t change signs):
→ -8r - 2 + 4r - 3
Combine like terms:
-8r + 4r = -4r
-2 - 3 = -5
✔ Final:
-4r - 5
---
3. (-z - 8) - (6z - 5)
Subtracting → flip signs in second group:
→ -z - 8 - 6z + 5
Combine:
-z - 6z = -7z
-8 + 5 = -3
✔ Final:
-7z - 3
---
4. (-s - 5) + (-2s + 2)
Add → keep all signs:
→ -s - 5 - 2s + 2
Combine:
-s - 2s = -3s
-5 + 2 = -3
✔ Final:
-3s - 3
---
5. (-7s + 4) - (-8s + 4)
Subtracting → flip signs in second group:
→ -7s + 4 + 8s - 4
Combine:
-7s + 8s = s
4 - 4 = 0
✔ Final:
s
---
6. (-4f + 9) - (8f + 9)
Subtracting → flip signs:
→ -4f + 9 - 8f - 9
Combine:
-4f - 8f = -12f
9 - 9 = 0
✔ Final:
-12f
---
7. (-8f) + (-f + 8)
Add → keep signs:
→ -8f - f + 8
Combine:
-8f - f = -9f
+8 stays
✔ Final:
-9f + 8
---
8. (4p - 4) + (-7p - 7)
Add → keep signs:
→ 4p - 4 - 7p - 7
Combine:
4p - 7p = -3p
-4 - 7 = -11
✔ Final:
-3p - 11
---
9. (7v - 9) - (6v + 9)
Subtracting → flip signs:
→ 7v - 9 - 6v - 9
Combine:
7v - 6v = v
-9 - 9 = -18
✔ Final:
v - 18
---
10. (-3g) + (5g - 5)
Add → keep signs:
→ -3g + 5g - 5
Combine:
-3g + 5g = 2g
-5 stays
✔ Final:
2g - 5
---
Final Answer:
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
Parent Tip: Review the logic above to help your child master the concept of adding linear expressions worksheet.
