Middle School Math Man problem cards featuring algebraic equations.

Let’s solve each equation one by one. We’ll isolate the variable n on one side and simplify step by step.

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1. 3n - 7 = 8

Add 7 to both sides:
→ 3n = 8 + 7 → 3n = 15
Divide both sides by 3:
→ n = 15 ÷ 3 → n = 5

✔ Check: 3(5) - 7 = 15 - 7 = 8 ✔️

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2. 34 = 5n + 9

Subtract 9 from both sides:
→ 34 - 9 = 5n → 25 = 5n
Divide both sides by 5:
→ n = 25 5 → n = 5

✔ Check: 5(5) + 9 = 25 + 9 = 34 ✔️

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3. -10 = -3n + 5

Subtract 5 from both sides:
→ -10 - 5 = -3n → -15 = -3n
Divide both sides by -3:
→ n = (-15) ÷ (-3) → n = 5

✔ Check: -3(5) + 5 = -15 + 5 = -10 ✔️

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4. -5n - 2 = -27

Add 2 to both sides:
→ -5n = -27 + 2 → -5n = -25
Divide both sides by -5:
→ n = (-25) ÷ (-5) → n = 5

✔ Check: -5(5) - 2 = -25 - 2 = -27 ✔️

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5. 12n - 18 = 42

Add 18 to both sides:
→ 12n = 42 + 18 → 12n = 60
Divide both sides by 12:
→ n = 60 ÷ 12 → n = 5

✔ Check: 12(5) - 18 = 60 - 18 = 42 ✔️

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6. 5n - 6 = -31

Add 6 to both sides:
→ 5n = -31 + 6 → 5n = -25
Divide both sides by 5:
→ n = -25 5 → n = -5

✔ Check: 5(-5) - 6 = -25 - 6 = -31 ✔️

Wait — this is different! Let me double-check:

Original: 5n - 6 = -31
Add 6: 5n = -25 → n = -5 ✔️ Correct.

But all others were 5? That’s okay — not all have to be same.

Hold on — let’s check problem #6 again in original image context. The user didn’t say they’re all supposed to be same, so we solve as given.

Actually — wait! Looking back at the grid, maybe I misread? No — let’s continue solving all correctly.

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7. 25 = -4n + 5

Subtract 5 from both sides:
→ 25 - 5 = -4n → 20 = -4n
Divide both sides by -4:
→ n = 20 (-4) → n = -5

✔ Check: -4(-5) + 5 = 20 + 5 = 25 ✔️

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8. 6n - 5 = -35

Add 5 to both sides:
→ 6n = -35 + 5 → 6n = -30
Divide both sides by 6:
→ n = -30 ÷ 6 → n = -5

✔ Check: 6(-5) - 5 = -30 - 5 = -35 ✔️

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9. 7n + 2 = -33

Subtract 2 from both sides:
→ 7n = -33 - 2 → 7n = -35
Divide both sides by 7:
→ n = -35 ÷ 7 → n = -5

✔ Check: 7(-5) + 2 = -35 + 2 = -33 ✔️

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10. 24 = -2n + 14

Subtract 14 from both sides:
→ 24 - 14 = -2n → 10 = -2n
Divide both sides by -2:
→ n = 10 ÷ (-2) → n = -5

✔ Check: -2(-5) + 14 = 10 + 14 = 24 ✔️

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So summarizing:

Equations 1–5 → n = 5
Equations 6–10 → n = -5

That’s correct based on calculations.

Final Answer:
The solutions are:
For equations 1 to 5: n = 5
For equations 6 to 10: n = -5