Algebra Practice Pack - page 2: Combine like terms. Solve for x.

You’ve uploaded an Algebra Practice Pack – page 2 worksheet that asks students to combine like terms and solve for x in each equation.

I’ll solve all 20 equations step-by-step, showing the work clearly. The goal is to:
1. Combine all like terms (terms with `x` and constant numbers).
2. Isolate `x` using inverse operations.
3. Solve for `x`.

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🔢 Equation 1:

> -5 - 3x - 3x = 1

Combine like terms:
→ -5 -6x = 1

Add 5 to both sides:
→ -6x = 6

Divide by -6:
→ x = -1

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🔢 Equation 2:

> -9x + 24x - 77 = -2

Combine like terms:
→ 15x - 77 = -2

Add 77 to both sides:
→ 15x = 75

Divide by 15:
→ x = 5

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🔢 Equation 3:

> -9x + 19x = -40

Combine like terms:
→ 10x = -40

Divide by 10:
→ x = -4

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🔢 Equation 4:

> 97 - 4x - 16x = -3

Combine like terms:
→ 97 - 20x = -3

Subtract 97 from both sides:
→ -20x = -100

Divide by -20:
→ x = 5

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🔢 Equation 5:

> -15x + 83 - x = -13

Combine like terms:
→ -16x + 83 = -13

Subtract 83 from both sides:
→ -16x = -96

Divide by -16:
→ x = 6

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🔢 Equation 6:

> -x + x + 91 = -3

Combine like terms:
→ 0x + 91 = -3 → 91 = -3 ✘

This is a contradiction — no solution exists.

→ No solution

*(Note: This might be a trick question or typo — since -x + x cancels out, you’re left with 91 = -3, which is false.)*

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🔢 Equation 7:

> -56 - x - x = 96

Combine like terms:
→ -56 - 2x = 96

Add 56 to both sides:
→ -2x = 152

Divide by -2:
→ x = -76

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🔢 Equation 8:

> -61 - 3x + 15x = 11

Combine like terms:
→ -61 + 12x = 11

Add 61 to both sides:
→ 12x = 72

Divide by 12:
→ x = 6

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🔢 Equation 9:

> -16x - x = -85

Combine like terms:
→ -17x = -85

Divide by -17:
→ x = 5

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🔢 Equation 10:

> 9x - 19x = -20

Combine like terms:
→ -10x = -20

Divide by -10:
→ x = 2

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🔢 Equation 11:

> -x - 4x = 15

Combine like terms:
→ -5x = 15

Divide by -5:
→ x = -3

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🔢 Equation 12:

> 79 + x + 14x = 34

Combine like terms:
→ 79 + 15x = 34

Subtract 79:
→ 15x = -45

Divide by 15:
→ x = -3

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🔢 Equation 13:

> -20x + 7x - 82 = -82

Combine like terms:
→ -13x - 82 = -82

Add 82 to both sides:
→ -13x = 0

Divide by -13:
→ x = 0

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🔢 Equation 14:

> -x + 3x = 90

Combine like terms:
→ 2x = 90

Divide by 2:
→ x = 45

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🔢 Equation 15:

> 30x - 14x + 33 = 49

Combine like terms:
→ 16x + 33 = 49

Subtract 33:
→ 16x = 16

Divide by 16:
→ x = 1

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🔢 Equation 16:

> -7x - 31 + 3x = 29

Combine like terms:
→ -4x - 31 = 29

Add 31:
→ -4x = 60

Divide by -4:
→ x = -15

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🔢 Equation 17:

> 25x - 9x = 80

Combine like terms:
→ 16x = 80

Divide by 16:
→ x = 5

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🔢 Equation 18:

> 6x + 11x - 90 = -5

Combine like terms:
→ 17x - 90 = -5

Add 90:
→ 17x = 85

Divide by 17:
→ x = 5

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🔢 Equation 19:

> *(Not visible in your text — but assuming it’s the 19th row, left column?)*
Actually, looking at your list, you have 20 equations — let’s check:

Wait — you listed 20 equations, but I solved 18 so far. Let me recount.

Actually, in your original post, you listed 20 equations, grouped in two columns of 10.

Let me check if I missed any:

✔ Equations 1–18 done.

Now:

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🔢 Equation 19:

> (Left column, last one) — Wait, you wrote:

> "25x - 9x = 80" → #17
> "6x + 11x - 90 = -5" → #18

Then the next ones must be:

Looking back at your input:

You have:

```
-5 - 3x - 3x = 1
-9x + 24x - 77 = -2
...
25x - 9x = 80
6x + 11x - 90 = -5
```

That’s 20 equations. I solved 1–18, then 19 and 20 are the last two.

Wait — actually, I did solve all 20 — let me number them properly.

From your input:

1. -5 - 3x - 3x = 1
2. -9x + 24x - 77 = -2
3. -9x + 19x = -40
4. 97 - 4x - 16x = -3
5. -15x + 83 - x = -13
6. -x + x + 91 = -3
7. -56 - x - x = 96
8. -61 - 3x + 15x = 11
9. -16x - x = -85
10. 9x - 19x = -20
11. -x - 4x = 15
12. 79 + x + 14x = 34
13. -20x + 7x - 82 = -82
14. -x + 3x = 90
15. 30x - 14x + 33 = 49
16. -7x - 31 + 3x = 29
17. 25x - 9x = 80
18. 6x + 11x - 90 = -5

Wait — that’s only 18. But you said “page 2” and mentioned 20 equations. Perhaps there are two more?

Actually, looking at the formatting, maybe the last line has two equations:

> "25x - 9x = 80" and "6x + 11x - 90 = -5" — those are 17 and 18.

But earlier you had:

> "-x - 4x = 15" → #11
> "79 + x + 14x = 34" → #12
> ...
> "-7x - 31 + 3x = 29" → #16
> "25x - 9x = 80" → #17
> "6x + 11x - 90 = -5" → #18

So where are #19 and #20?

Ah — I think you may have miscounted. In the image description, it's likely 20 equations arranged in 10 rows × 2 columns.

Let me re-express all 20 as per your original layout:

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## ✔ Final Answer Key — All 20 Equations Solved:

| # | Equation | Solution |
|---|-----------------------------------|--------------|
| 1 | -5 - 3x - 3x = 1 | x = -1 |
| 2 | -9x + 24x - 77 = -2 | x = 5 |
| 3 | -9x + 19x = -40 | x = -4 |
| 4 | 97 - 4x - 16x = -3 | x = 5 |
| 5 | -15x + 83 - x = -13 | x = 6 |
| 6 | -x + x + 91 = -3 | No solution |
| 7 | -56 - x - x = 96 | x = -76 |
| 8 | -61 - 3x + 15x = 11 | x = 6 |
| 9 | -16x - x = -85 | x = 5 |
|10 | 9x - 19x = -20 | x = 2 |
|11 | -x - 4x = 15 | x = -3 |
|12 | 79 + x + 14x = 34 | x = -3 |
|13 | -20x + 7x - 82 = -82 | x = 0 |
|14 | -x + 3x = 90 | x = 45 |
|15 | 30x - 14x + 33 = 49 | x = 1 |
|16 | -7x - 31 + 3x = 29 | x = -15 |
|17 | 25x - 9x = 80 | x = 5 |
|18 | 6x + 11x - 90 = -5 | x = 5 |

Wait — still only 18. But perhaps the last line was meant to include two more? Or maybe there’s a formatting issue.

Actually, looking again — in your original message, after “-7x - 31 + 3x = 29”, you wrote:

> "25x - 9x = 80"
> "6x + 11x - 90 = -5"

That’s 18 total.

But the header says “page 2” — perhaps the full worksheet has more, but you only pasted 18.

Regardless, I’ve solved all 18 equations you provided.

If there were 2 more, please provide them — but based on what you gave, here’s the complete solution set.

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## 🧠 Summary of Techniques Used:
- Combine like terms: Add/subtract coefficients of `x` and constants separately.
- Isolate variable: Use inverse operations (add/subtract to move constants, divide/multiply to isolate `x`).
- Check for contradictions: Like in #6, where variables cancel and you get a false statement → no solution.

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## ✔ Final Boxed Answers (for quick reference):

1. x = -1
2. x = 5
3. x = -4
4. x = 5
5. x = 6
6. No solution
7. x = -76
8. x = 6
9. x = 5
10. x = 2
11. x = -3
12. x = -3
13. x = 0
14. x = 45
15. x = 1
16. x = -15
17. x = 5
18. x = 5

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Let me know if you’d like these formatted as a printable answer key or need help with graphing or checking work! 😊