Algebra worksheet for combining like terms with equations.

Let’s solve each equation one by one. We’ll combine like terms first, then isolate the variable x.

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1. 3x + 22 - 14x = 0

Combine x terms:
3x - 14x = -11x
So: -11x + 22 = 0
Subtract 22 from both sides:
-11x = -22
Divide by -11:
→ x = 2

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2. 2x + x - 39 = -36

Combine x terms:
2x + x = 3x
So: 3x - 39 = -36
Add 39 to both sides:
3x = 3
Divide by 3:
→ x = 1

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3. -4x + 40 - 12x = -24

Combine x terms:
-4x -12x = -16x
So: -16x + 40 = -24
Subtract 40 from both sides:
-16x = -64
Divide by -16:
→ x = 4

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4. 37 + 3x + 5x = 101

Combine x terms:
3x + 5x = 8x
So: 37 + 8x = 101
Subtract 37 from both sides:
8x = 64
Divide by 8:
→ x = 8

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5. -4x + 16 - 6x = 46

Combine x terms:
-4x -6x = -10x
So: -10x + 16 = 46
Subtract 16 from both sides:
-10x = 30
Divide by -10:
→ x = -3

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6. -7x + 18x = 11

Combine x terms:
-7x + 18x = 11x
So: 11x = 11
Divide by 11:
→ x = 1

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7. 14x + 58 - 4x = 8

Combine x terms:
14x - 4x = 10x
So: 10x + 58 = 8
Subtract 58 from both sides:
10x = -50
Divide by 10:
→ x = -5

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8. -2x - 6x + 26 = 50

Combine x terms:
-2x -6x = -8x
So: -8x + 26 = 50
Subtract 26 from both sides:
-8x = 24
Divide by -8:
→ x = -3

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9. -44 + 4x + 15x = 51

Combine x terms:
4x + 15x = 19x
So: -44 + 19x = 51
Add 44 to both sides:
19x = 95
Divide by 19:
→ x = 5

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10. -4x + 20x + 40 = 8

Combine x terms:
-4x + 20x = 16x
So: 16x + 40 = 8
Subtract 40 from both sides:
16x = -32
Divide by 16:
→ x = -2

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11. -79 - 4x + x = -13

Combine x terms:
-4x + x = -3x
So: -79 - 3x = -13
Add 79 to both sides:
-3x = 66
Divide by -3:
→ x = -22

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12. -55 - x - 7x = -3

Combine x terms:
-x -7x = -8x
So: -55 -8x = -3
Add 55 to both sides:
-8x = 52
Divide by -8:
→ x = -6.5 or -13/2

*(We can leave as fraction if needed — but decimal is fine too)*

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Now let’s do the second column:

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13. 10x + 3x - 63 = 2

Combine x terms:
10x + 3x = 13x
So: 13x - 63 = 2
Add 63 to both sides:
13x = 65
Divide by 13:
→ x = 5

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14. x - 81 - 21x = -1

Combine x terms:
x -21x = -20x
So: -20x -81 = -1
Add 81 to both sides:
-20x = 80
Divide by -20:
→ x = -4

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15. -41 - 5x + 15x = -9

Combine x terms:
-5x +15x = 10x
So: -41 + 10x = -9
Add 41 to both sides:
10x = 32
Divide by 10:
→ x = 3.2 or 16/5

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16. 50 + 9x - 19x = -10

Combine x terms:
9x -19x = -10x
So: 50 -10x = -10
Subtract 50 from both sides:
-10x = -60
Divide by -10:
→ x = 6

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17. 5x + 8x - 89 = -4

Combine x terms:
5x +8x = 13x
So: 13x -89 = -4
Add 89 to both sides:
13x = 85
Divide by 13:
→ x = 85/13 ≈ 6.538... → Let’s keep exact: x = 85/13

Wait — double-check:

13x = 85 → yes, 85 ÷ 13 doesn’t simplify → so x = 85/13

But maybe I made a mistake? Let me check original:

5x + 8x = 13x; 13x -89 = -4 → 13x = 85 → correct.

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18. 2 + 7x - 16x = -70

Combine x terms:
7x -16x = -9x
So: 2 -9x = -70
Subtract 2 from both sides:
-9x = -72
Divide by -9:
→ x = 8

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19. 2x + x - 59 = 10

Combine x terms:
2x + x = 3x
So: 3x -59 = 10
Add 59 to both sides:
3x = 69
Divide by 3:
→ x = 23

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20. 18 - x - 2x = 63

Combine x terms:
-x -2x = -3x
So: 18 -3x = 63
Subtract 18 from both sides:
-3x = 45
Divide by -3:
→ x = -15

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21. 93 - 28x + 12x = -51

Combine x terms:
-28x +12x = -16x
So: 93 -16x = -51
Subtract 93 from both sides:
-16x = -144
Divide by -16:
→ x = 9

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22. 8x + 12x - 100 = ?

Wait — this one says “= ?” — probably typo? Looking back at image description — it should be equal to something.

Actually, looking again — in your list it says:

> 8x + 12x - 100 =

Hmm — incomplete? But in original problem set, likely it's meant to be solved for x with an equals sign. Wait — perhaps it's missing RHS?

Wait — checking user input:

In the original text you provided:

“8x + 12x - 100 = ” — no right side? That can't be.

Wait — actually, looking carefully at your message:

You wrote:

```
8x + 12x - 100 =
```

That seems incomplete. But in standard worksheets, every equation has an equals and a number.

Perhaps it’s a typo and should be = 0? Or maybe = something else?

Wait — let me recheck your full input:

Looking at your original post:

Under third column, last few:

> 57 + 2x + 14x = -89
> -2x - 15x + 55 = -13
> 10x + 31 - 4x = 7

And before that:

> 8x + 12x - 100 =

Ah — probably it’s supposed to be = 0? Or maybe = -something?

Wait — actually, in many such sheets, sometimes they forget to write the RHS. But since all others have numbers, perhaps it’s a mistake.

Alternatively — maybe it’s = 0? Let’s assume that for now — because otherwise we can’t solve.

But wait — let me look again at your exact text:

You wrote:

```
8x + 12x - 100 =
```

No value after equals. This must be an error.

But in context of worksheet, perhaps it’s meant to be = 0? Or maybe = -20? Not sure.

Wait — actually, looking at pattern — maybe it’s = -20? No.

Alternatively — perhaps it’s a misformatting and it’s supposed to be part of next line? Unlikely.

To proceed, I’ll assume it’s = 0 (common default). If not, student should clarify.

So assuming:

22. 8x + 12x - 100 = 0

Combine x terms:
8x +12x = 20x
So: 20x -100 = 0
Add 100:
20x = 100
Divide by 20:
→ x = 5

*(If actual RHS is different, answer changes — but based on common patterns, this is reasonable.)*

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23. -x + 6x = 9

Combine x terms:
-x +6x = 5x
So: 5x = 9
Divide by 5:
→ x = 9/5 = 1.8

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24. -17x - 2x = -38

Combine x terms:
-17x -2x = -19x
So: -19x = -38
Divide by -19:
→ x = 2

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Third column:

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25. -6x - 13 - 9x = -31

Combine x terms:
-6x -9x = -15x
So: -15x -13 = -31
Add 13 to both sides:
-15x = -18
Divide by -15:
→ x = 18/15 = 6/5 = 1.2

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26. 23 + 15x - 4x = 12

Combine x terms:
15x -4x = 11x
So: 23 + 11x = 12
Subtract 23:
11x = -11
Divide by 11:
→ x = -1

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27. 85 - 2x - 3x = 40

Combine x terms:
-2x -3x = -5x
So: 85 -5x = 40
Subtract 85:
-5x = -45
Divide by -5:
→ x = 9

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28. 91 + 17x - 4x = 78

Combine x terms:
17x -4x = 13x
So: 91 +13x = 78
Subtract 91:
13x = -13
Divide by 13:
→ x = -1

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29. -2x - 87 - 7x = -15

Combine x terms:
-2x -7x = -9x
So: -9x -87 = -15
Add 87:
-9x = 72
Divide by -9:
→ x = -8

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30. -x + 6x - 69 = -6

Combine x terms:
-x +6x = 5x
So: 5x -69 = -6
Add 69:
5x = 63
Divide by 5:
→ x = 63/5 = 12.6

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31. 16x - 13 - 36x = -13

Combine x terms:
16x -36x = -20x
So: -20x -13 = -13
Add 13 to both sides:
-20x = 0
Divide by -20:
→ x = 0

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32. 50 + 11x - 26x = -70

Combine x terms:
11x -26x = -15x
So: 50 -15x = -70
Subtract 50:
-15x = -120
Divide by -15:
→ x = 8

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33. -11x - 2x = -52

Combine x terms:
-11x -2x = -13x
So: -13x = -52
Divide by -13:
→ x = 4

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34. 57 + 2x + 14x = -89

Combine x terms:
2x +14x = 16x
So: 57 +16x = -89
Subtract 57:
16x = -146
Divide by 16:
→ x = -146/16 = -73/8 = -9.125

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35. -2x - 15x + 55 = -13

Combine x terms:
-2x -15x = -17x
So: -17x +55 = -13
Subtract 55:
-17x = -68
Divide by -17:
→ x = 4

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36. 10x + 31 - 4x = 7

Combine x terms:
10x -4x = 6x
So: 6x +31 = 7
Subtract 31:
6x = -24
Divide by 6:
→ x = -4

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Now, compiling all answers in order:

Column 1 (left):

1. x = 2
2. x = 1
3. x = 4
4. x = 8
5. x = -3
6. x = 1
7. x = -5
8. x = -3
9. x = 5
10. x = -2
11. x = -22
12. x = -6.5 or -13/2

Column 2 (middle):

13. x = 5
14. x = -4
15. x = 3.2 or 16/5
16. x = 6
17. x = 85/13
18. x = 8
19. x = 23
20. x = -15
21. x = 9
22. x = 5 *(assumed =0)*
23. x = 1.8 or 9/5
24. x = 2

Column 3 (right):

25. x = 1.2 or 6/5
26. x = -1
27. x = 9
28. x = -1
29. x = -8
30. x = 12.6 or 63/5
31. x = 0
32. x = 8
33. x = 4
34. x = -9.125 or -73/8
35. x = 4
36. x = -4

Note: For #22, if the intended RHS was not 0, the answer will differ. Please verify the original problem.

Final Answer:
[2, 1, 4, 8, -3, 1, -5, -3, 5, -2, -22, -6.5, 5, -4, 3.2, 6, 85/13, 8, 23, -15, 9, 5, 1.8, 2, 1.2, -1, 9, -1, -8, 12.6, 0, 8, 4, -9.125, 4, -4]