Multiplying Polynomials Answer Key - Kuta Software - Infinite ... - Free Printable

Let’s solve each equation step by step. We’ll isolate the variable (usually x or y) on one side of the equation.

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1. 3x + 5 = 20

Subtract 5 from both sides:
→ 3x = 15

Divide both sides by 3:
→ x = 5

✔ Check: 3(5) + 5 = 15 + 5 = 20 → Correct

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2. 4y - 7 = 9

Add 7 to both sides:
→ 4y = 16

Divide by 4:
→ y = 4

✔ Check: 4(4) - 7 = 16 - 7 = 9 → Correct

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3. 2(x + 3) = 14

First, divide both sides by 2:
→ x + 3 = 7

Subtract 3:
→ x = 4

✔ Check: 2(4 + 3) = 2(7) = 14 → Correct

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4. 5x - 2 = 3x + 8

Subtract 3x from both sides:
→ 2x - 2 = 8

Add 2 to both sides:
→ 2x = 10

Divide by 2:
→ x = 5

✔ Check: Left: 5(5)-2=25-2=23; Right: 3(5)+8=15+8=23 → Correct

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5. 7 - 2x = 1

Subtract 7 from both sides:
→ -2x = -6

Divide by -2:
→ x = 3

✔ Check: 7 - 2(3) = 7 - 6 = 1 → Correct

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6. 3(y - 4) = 2y + 1

Expand left side:
→ 3y - 12 = 2y + 1

Subtract 2y from both sides:
→ y - 12 = 1

Add 12:
→ y = 13

✔ Check: Left: 3(13-4)=3(9)=27; Right: 2(13)+1=26+1=27 → Correct

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7. ½x + 4 = 7

Subtract 4:
→ ½x = 3

Multiply both sides by 2:
→ x = 6

✔ Check: ½(6) + 4 = 3 + 4 = 7 → Correct

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8. 2x + 3 = 5x - 6

Subtract 2x from both sides:
→ 3 = 3x - 6

Add 6:
→ 9 = 3x

Divide by 3:
→ x = 3

✔ Check: Left: 2(3)+3=6+3=9; Right: 5(3)-6=15-6=9 → Correct

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9. 4(x - 2) = 3x + 1

Expand left:
→ 4x - 8 = 3x + 1

Subtract 3x:
→ x - 8 = 1

Add 8:
→ x = 9

✔ Check: Left: 4(9-2)=4(7)=28; Right: 3(9)+1=27+1=28 → Correct

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10. 6 - 3y = 2y + 1

Add 3y to both sides:
→ 6 = 5y + 1

Subtract 1:
→ 5 = 5y

Divide by 5:
→ y = 1

✔ Check: Left: 6 - 3(1)=3; Right: 2(1)+1=3 → Correct

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Final Answer:
1. x = 5
2. y = 4
3. x = 4
4. x = 5
5. x = 3
6. y = 13
7. x = 6
8. x = 3
9. x = 9
10. y = 1