Sure! Let’s solve each problem step by step. The worksheet has two sections:
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##
Section 1: Solve each equation
These are simple linear equations with one variable. We combine like terms and then isolate the variable.
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1. 2a + a = 18
Combine like terms:
→ 3a = 18
Divide both sides by 3:
→
a = 6
✔ Answer: a = 6
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2. 4a + 3a = -21
Combine like terms:
→ 7a = -21
Divide both sides by 7:
→
a = -3
✔ Answer: a = -3
---
3. 5x - 3x = -20
Combine like terms:
→ 2x = -20
Divide both sides by 2:
→
x = -10
✔ Answer: x = -10
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4. -9x + 4x = -15
Combine like terms:
→ -5x = -15
Divide both sides by -5:
→
x = 3
✔ Answer: x = 3
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5. 2b + 6b = -24
Combine like terms:
→ 8b = -24
Divide both sides by 8:
→
b = -3
✔ Answer: b = -3
---
6. 7x - 3x = -32
Combine like terms:
→ 4x = -32
Divide both sides by 4:
→
x = -8
✔ Answer: x = -8
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7. 5x + 4x = -27
Combine like terms:
→ 9x = -27
Divide both sides by 9:
→
x = -3
✔ Answer: x = -3
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##
Section 2: Find each square root
We are finding the
principal (non-negative) square root of each number — that is, the positive number that, when squared, gives the original number.
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8. √64
What number squared equals 64?
→ 8 × 8 = 64
→
√64 = 8
✔ Answer: 8
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9. √36
→ 6 × 6 = 36
→
√36 = 6
✔ Answer: 6
---
10. √25
→ 5 × 5 = 25
→
√25 = 5
✔ Answer: 5
---
11. √81
→ 9 × 9 = 81
→
√81 = 9
✔ Answer: 9
---
12. √144
→ 12 × 12 = 144
→
√144 = 12
✔ Answer: 12
---
13. √121
→ 11 × 11 = 121
→
√121 = 11
✔ Answer: 11
---
14. √0
→ 0 × 0 = 0
→
√0 = 0
✔ Answer: 0
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##
✔ Final Answers Summary:
Equations:
1.
a = 6
2.
a = -3
3.
x = -10
4.
x = 3
5.
b = -3
6.
x = -8
7.
x = -3
Square Roots:
8.
8
9.
6
10.
5
11.
9
12.
12
13.
11
14.
0
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Let me know if you’d like to see these explained in more detail or want practice problems! 😊
Parent Tip: Review the logic above to help your child master the concept of pre algebra worksheets pdf.
