Let’s solve each problem one by one. We’ll simplify the algebraic expressions by combining like terms and using the distributive property when needed.
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1) -6q + 7 - 2 + 4q
Step 1: Combine the q terms → -6q + 4q =
-2q
Step 2: Combine the numbers → 7 - 2 =
5
Final:
-2q + 5
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2) 2b - 3b + 9 + 5
Step 1: Combine b terms → 2b - 3b =
-b
Step 2: Combine numbers → 9 + 5 =
14
Final:
-b + 14
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3) -3(9b + 4)
Use distributive property: multiply -3 by each term inside parentheses
→ -3 × 9b =
-27b
→ -3 × 4 =
-12
Final:
-27b - 12
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4) 9(8f + 3) - 7f
Step 1: Distribute 9 → 9×8f =
72f, 9×3 =
27 → so we have 72f + 27 - 7f
Step 2: Combine f terms → 72f - 7f =
65f
Step 3: Keep the constant →
+27
Final:
65f + 27
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5) 3 - 9h - 2 + 7h
Step 1: Combine h terms → -9h + 7h =
-2h
Step 2: Combine numbers → 3 - 2 =
1
Final:
-2h + 1
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6) 3(5g - 7) - 8
Step 1: Distribute 3 → 3×5g =
15g, 3×(-7) =
-21 → so we have 15g - 21 - 8
Step 2: Combine constants → -21 - 8 =
-29
Final:
15g - 29
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7) -2(3 - 6r)
Distribute -2 to both terms:
→ -2 × 3 =
-6
→ -2 × (-6r) =
+12r (negative times negative is positive)
Final:
12r - 6
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8) 3q - 5 - 9q - 2
Step 1: Combine q terms → 3q - 9q =
-6q
Step 2: Combine numbers → -5 - 2 =
-7
Final:
-6q - 7
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9) 6(-7 + 5y) - 9y
Step 1: Distribute 6 → 6×(-7) =
-42, 6×5y =
30y → so we have -42 + 30y - 9y
Step 2: Combine y terms → 30y - 9y =
21y
Step 3: Keep constant →
-42
Final:
21y - 42
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10) -8(7y + 6)
Distribute -8:
→ -8 × 7y =
-56y
→ -8 × 6 =
-48
Final:
-56y - 48
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Final Answer:
1) -2q + 5
2) -b + 14
3) -27b - 12
4) 65f + 27
5) -2h + 1
6) 15g - 29
7) 12r - 6
8) -6q - 7
9) 21y - 42
10) -56y - 48
Parent Tip: Review the logic above to help your child master the concept of expression worksheet 7th grade.
