Algebra Practice Problems #2: Solve 10 equations and simplify answers as fractions or mixed numbers.

Sure! Let’s solve each of the 10 algebraic equations step by step. The goal is to isolate the variable x and simplify the answer — reducing fractions and converting them to mixed numbers if needed. Some may involve square roots, as noted.

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Problem 1:

> 2x² + 4(x² + 3) - 2 = 22

Step 1: Distribute the 4
→ 2x² + 4x² + 12 - 2 = 22

Step 2: Combine like terms
→ (2x² + 4x²) + (12 - 2) = 22
→ 6x² + 10 = 22

Step 3: Subtract 10 from both sides
→ 6x² = 12

Step 4: Divide by 6
→ x² = 2

Step 5: Take square root
→ x = ±√2

✔ Answer: x = √2 or x = -√2

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Problem 2:

> 3x + 2(x - 4) = 20

Step 1: Distribute the 2
→ 3x + 2x - 8 = 20

Step 2: Combine like terms
→ 5x - 8 = 20

Step 3: Add 8 to both sides
→ 5x = 28

Step 4: Divide by 5
→ x = 28/5

Step 5: Convert to mixed number
→ 28 ÷ 5 = 5 with remainder 3 → 5 3/5

✔ Answer: x = 5 3/5

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Problem 3:

> 13 - 3(x + 2) + 5x = 29

Step 1: Distribute the -3
→ 13 - 3x - 6 + 5x = 29

Step 2: Combine like terms
→ (-3x + 5x) + (13 - 6) = 29
→ 2x + 7 = 29

Step 3: Subtract 7
→ 2x = 22

Step 4: Divide by 2
→ x = 11

✔ Answer: x = 11

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Problem 4:

> 17 + 2(4 + 2x²) = 33

Step 1: Distribute the 2
→ 17 + 8 + 4x² = 33

Step 2: Combine constants
→ 25 + 4x² = 33

Step 3: Subtract 25
→ 4x² = 8

Step 4: Divide by 4
→ x² = 2

Step 5: Square root
→ x = ±√2

✔ Answer: x = √2 or x = -√2

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Problem 5:

> 5x - 12 + 3(x - 1) = -14

Step 1: Distribute the 3
→ 5x - 12 + 3x - 3 = -14

Step 2: Combine like terms
→ (5x + 3x) + (-12 - 3) = -14
→ 8x - 15 = -14

Step 3: Add 15 to both sides
→ 8x = 1

Step 4: Divide by 8
→ x = 1/8

✔ Answer: x = 1/8

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Problem 6:

> 3(x² + 2) - 5 = 28

Step 1: Distribute the 3
→ 3x² + 6 - 5 = 28

Step 2: Simplify
→ 3x² + 1 = 28

Step 3: Subtract 1
→ 3x² = 27

Step 4: Divide by 3
→ x² = 9

Step 5: Square root
→ x = ±3

✔ Answer: x = 3 or x = -3

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Problem 7:

> 6(x² - 4) + 8 - 2x² = 7

Step 1: Distribute the 6
→ 6x² - 24 + 8 - 2x² = 7

Step 2: Combine like terms
→ (6x² - 2x²) + (-24 + 8) = 7
→ 4x² - 16 = 7

Step 3: Add 16
→ 4x² = 23

Step 4: Divide by 4
→ x² = 23/4

Step 5: Square root
→ x = ±√(23/4) = ±(√23)/2

✔ Answer: x = (√23)/2 or x = -(√23)/2

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Problem 8:

> 17 - 2x + 3 + x = 11

Step 1: Combine like terms
→ (-2x + x) + (17 + 3) = 11
→ -x + 20 = 11

Step 2: Subtract 20
→ -x = -9

Step 3: Multiply by -1
→ x = 9

✔ Answer: x = 9

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Problem 9:

> 10 + 5x - 4(x - 2) = 31

Step 1: Distribute the -4
→ 10 + 5x - 4x + 8 = 31

Step 2: Combine like terms
→ (5x - 4x) + (10 + 8) = 31
→ x + 18 = 31

Step 3: Subtract 18
→ x = 13

✔ Answer: x = 13

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Problem 10:

> 4x + 3(x - 3) = 26

Step 1: Distribute the 3
→ 4x + 3x - 9 = 26

Step 2: Combine like terms
→ 7x - 9 = 26

Step 3: Add 9
→ 7x = 35

Step 4: Divide by 7
→ x = 5

✔ Answer: x = 5

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## ✔ Final Answers Summary:

1. x = ±√2
2. x = 5 3/5
3. x = 11
4. x = ±√2
5. x = 1/8
6. x = ±3
7. x = ±(√23)/2
8. x = 9
9. x = 13
10. x = 5

Let me know if you’d like to see any step explained in more detail!