Math worksheet titled "Modeling Linear Equations #2" with problems and handwritten solutions in purple ink.

Let’s solve each problem step by step. We’ll use the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right) and simplify carefully.

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1. 28 - [4 + 3(7 - 5)] ÷ 2

First, do inside parentheses:
7 - 5 = 2
Now: 28 - [4 + 3×2] ÷ 2
Multiply: 3×2 = 6
Now: 28 - [4 + 6] ÷ 2 → 28 - [10] ÷ 2
Divide: 10 ÷ 2 = 5
Subtract: 28 - 5 = 23

✔ Final Answer for #1: 23

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2. 9² - 3[2(4 - 1) + 5]

Exponent first: 9² = 81
Inside brackets: 4 - 1 = 3
Then: 2×3 = 6
Then: 6 + 5 = 11
Now: 3×11 = 33
Finally: 81 - 33 = 48

✔ Final Answer for #2: 48

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3. 4[5 + 2(3 - 1)] - 3(4 + 1)

Parentheses: 3 - 1 = 2; 4 + 1 = 5
Multiply: 2×2 = 4; 3×5 = 15
Inside bracket: 5 + 4 = 9
Multiply: 4×9 = 36
Subtract: 36 - 15 = 21

✔ Final Answer for #3: 21

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4. 8 × 3² - 4 × 2³

Exponents: 3² = 9; 2³ = 8
Multiply: 8×9 = 72; 4×8 = 32
Subtract: 72 - 32 = 40

✔ Final Answer for #4: 40

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5. (10 - 4)² ÷ 3 + 2(5 - 1)

Parentheses: 10 - 4 = 6; 5 - 1 = 4
Exponent: 6² = 36
Divide: 36 ÷ 3 = 12
Multiply: 2×4 = 8
Add: 12 + 8 = 20

✔ Final Answer for #5: 20

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6. 5[2(3 + 1) - 4] + 3(6 - 2)

Parentheses: 3 + 1 = 4; 6 - 2 = 4
Multiply: 2×4 = 8; 3×4 = 12
Inside bracket: 8 - 4 = 4
Multiply: 5×4 = 20
Add: 20 + 12 = 32

✔ Final Answer for #6: 32

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7. 100 ÷ [2(3 + 2) - 5] + 4

Parentheses: 3 + 2 = 5
Multiply: 2×5 = 10
Bracket: 10 - 5 = 5
Divide: 100 ÷ 5 = 20
Add: 20 + 4 = 24

✔ Final Answer for #7: 24

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8. 3{2[5 + 3(4 - 2)] - 1}

Innermost: 4 - 2 = 2
Multiply: 3×2 = 6
Bracket: 5 + 6 = 11
Multiply: 2×11 = 22
Brace: 22 - 1 = 21
Multiply: 3×21 = 63

✔ Final Answer for #8: 63

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9. 12 + 3[4(5 - 2) - 6] ÷ 2

Parentheses: 5 - 2 = 3
Multiply: 4×3 = 12
Bracket: 12 - 6 = 6
Multiply: 3×6 = 18
Divide: 18 ÷ 2 = 9
Add: 12 + 9 = 21

✔ Final Answer for #9: 21

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10. 2{3[4(5 - 1) - 8] + 2} - 5

Innermost: 5 - 1 = 4
Multiply: 4×4 = 16
Bracket: 16 - 8 = 8
Multiply: 3×8 = 24
Brace: 24 + 2 = 26
Multiply: 2×26 = 52
Subtract: 52 - 5 = 47

✔ Final Answer for #10: 47

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11. 4[3(2 + 1) - 5] + 2[6 - 3(2 - 1)]

First part: 2 + 1 = 3 → 3×3 = 9 → 9 - 5 = 4 → 4×4 = 16
Second part: 2 - 1 = 1 → 3×1 = 3 → 6 - 3 = 3 → 2×3 = 6
Add: 16 + 6 = 22

✔ Final Answer for #11: 22

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12. {5[2(3 + 1) - 4] + 3} ÷ 2

Parentheses: 3 + 1 = 4
Multiply: 2×4 = 8
Bracket: 8 - 4 = 4
Multiply: 5×4 = 20
Brace: 20 + 3 = 23
Divide: 23 ÷ 2 = 11.5

✔ Final Answer for #12: 11.5

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13. 2[3(4 + 2) - 5] + 4[2(3 - 1) + 1]

First part: 4 + 2 = 6 → 3×6 = 18 → 18 - 5 = 13 → 2×13 = 26
Second part: 3 - 1 = 2 → 2×2 = 4 → 4 + 1 = 5 → 4×5 = 20
Add: 26 + 20 = 46

✔ Final Answer for #13: 46

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14. 3{2[5 + 3(4 - 2)] - 1} + 4

Same as #8 but add 4 at end. From #8 we had 63.
So: 63 + 4 = 67

Wait — let’s recalculate to be sure:

Innermost: 4 - 2 = 2
Multiply: 3×2 = 6
Bracket: 5 + 6 = 11
Multiply: 2×11 = 22
Brace: 22 - 1 = 21
Multiply: 3×21 = 63
Add: 63 + 4 = 67

✔ Final Answer for #14: 67

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15. 5[2(3 + 1) - 4] + 3[6 - 2(3 - 1)]

First part: 3 + 1 = 4 → 2×4 = 8 → 8 - 4 = 4 → 5×4 = 20
Second part: 3 - 1 = 2 → 2×2 = 4 → 6 - 4 = 2 → 3×2 = 6
Add: 20 + 6 = 26

✔ Final Answer for #15: 26

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Final Answers:

1. 23
2. 48
3. 21
4. 40
5. 20
6. 32
7. 24
8. 63
9. 21
10. 47
11. 22
12. 11.5
13. 46
14. 67
15. 26