Let’s solve each problem step by step.
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Part 1: Solve each equation
These are simple linear equations. We combine like terms on the left, then divide to isolate the variable.
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1. 2a + a = 18
Combine: 2a + a = 3a
So: 3a = 18
Divide both sides by 3: a = 6
✔ Check: 2(6) + 6 = 12 + 6 = 18 → Correct
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2. 4a + 3a = -21
Combine: 7a = -21
Divide by 7: a = -3
✔ Check: 4(-3) + 3(-3) = -12 + (-9) = -21 → Correct
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3. 5x - 3x = -20
Combine: 2x = -20
Divide by 2: x = -10
✔ Check: 5(-10) - 3(-10) = -50 + 30 = -20 → Correct
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4. -9x + 4x = -15
Combine: -5x = -15
Divide by -5: x = 3
✔ Check: -9(3) + 4(3) = -27 + 12 = -15 → Correct
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5. 2b + 6b = -24
Combine: 8b = -24
Divide by 8: b = -3
✔ Check: 2(-3) + 6(-3) = -6 + (-18) = -24 → Correct
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6. 7x - 3x = -32
Combine: 4x = -32
Divide by 4: x = -8
✔ Check: 7(-8) - 3(-8) = -56 + 24 = -32 → Correct
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7. 5x + 4x = -27
Combine: 9x = -27
Divide by 9: x = -3
✔ Check: 5(-3) + 4(-3) = -15 + (-12) = -27 → Correct
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Part 2: Find each square root
Square root means: what number times itself gives this?
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8. √64
What × itself = 64? → 8 × 8 = 64 → So √64 = 8
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9. √36
6 × 6 = 36 → √36 = 6
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10. √25
5 × 5 = 25 → √25 = 5
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11. 81
9 × 9 = 81 → √81 = 9
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12. √144
12 × 12 = 144 → √144 = 12
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13. √121
11 × 11 = 121 → √121 = 11
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14. √0
0 × 0 = 0 → √0 = 0
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All answers verified.
Final Answer:
1. a = 6
2. a = -3
3. x = -10
4. x = 3
5. b = -3
6. x = -8
7. x = -3
8. 8
9. 6
10. 5
11. 9
12. 12
13. 11
14. 0
Parent Tip: Review the logic above to help your child master the concept of math pre algebra worksheet.
