Simplify each expression by combining like terms on this math worksheet.

Let's solve each expression step by step by combining like terms. The goal is to simplify each algebraic expression by combining the coefficients of the same variable (usually $ x $) and simplifying constants.

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1) $ 13x + (4x - 4 - x) $

First, simplify inside the parentheses:
$$
4x - 4 - x = (4x - x) - 4 = 3x - 4
$$
Now add to $ 13x $:
$$
13x + 3x - 4 = 16x - 4
$$
✔ Answer: $ 16x - 4 $

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2) $ 17x + 4(3x - 4 + x) $

Simplify inside parentheses:
$$
3x + x - 4 = 4x - 4
$$
Now distribute the 4:
$$
4(4x - 4) = 16x - 16
$$
Add to $ 17x $:
$$
17x + 16x - 16 = 33x - 16
$$
✔ Answer: $ 33x - 16 $

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3) $ 3x - 4x $

Combine like terms:
$$
(3 - 4)x = -x
$$
✔ Answer: $ -x $

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4) $ 7x - 3x $

$$
(7 - 3)x = 4x
$$
✔ Answer: $ 4x $

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5) $ 10x - 9x $

$$
(10 - 9)x = x
$$
✔ Answer: $ x $

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6) $ 10x + (-4)(4x - 4 + x) $

Simplify inside parentheses:
$$
4x + x - 4 = 5x - 4
$$
Now multiply by $-4$:
$$
(-4)(5x - 4) = -20x + 16
$$
Add to $ 10x $:
$$
10x - 20x + 16 = -10x + 16
$$
✔ Answer: $ -10x + 16 $

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7) $ 14x + 2x - 2 $

Combine $ x $-terms:
$$
14x + 2x = 16x
$$
So:
$$
16x - 2
$$
✔ Answer: $ 16x - 2 $

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8) $ 18x + (2x - 2 - x) $

Simplify inside parentheses:
$$
2x - x - 2 = x - 2
$$
Now add:
$$
18x + x - 2 = 19x - 2
$$
✔ Answer: $ 19x - 2 $

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9) $ 20x + 2(3x - 2 + x) $

Inside parentheses:
$$
3x + x - 2 = 4x - 2
$$
Multiply by 2:
$$
2(4x - 2) = 8x - 4
$$
Add to $ 20x $:
$$
20x + 8x - 4 = 28x - 4
$$
✔ Answer: $ 28x - 4 $

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10) $ 16x + 3x - 3 $

$$
(16x + 3x) - 3 = 19x - 3
$$
✔ Answer: $ 19x - 3 $

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11) $ 18x + (-3)(2x - 3 + x) $

Simplify inside:
$$
2x + x - 3 = 3x - 3
$$
Multiply by $-3$:
$$
(-3)(3x - 3) = -9x + 9
$$
Add to $ 18x $:
$$
18x - 9x + 9 = 9x + 9
$$
✔ Answer: $ 9x + 9 $

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12) $ 21x + (-3)(3x - 3 + x) $

Inside:
$$
3x + x - 3 = 4x - 3
$$
Multiply by $-3$:
$$
(-3)(4x - 3) = -12x + 9
$$
Add to $ 21x $:
$$
21x - 12x + 9 = 9x + 9
$$
✔ Answer: $ 9x + 9 $

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13) $ 13x + (-3)(2x - 3 + x) $

Same as #11 and #12:
Inside: $ 3x - 3 $
Multiply: $-3(3x - 3) = -9x + 9$
Add: $ 13x - 9x + 9 = 4x + 9 $
✔ Answer: $ 4x + 9 $

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14) $ 8x + (3x - 3 - x) $

Inside: $ 3x - x - 3 = 2x - 3 $
Add to $ 8x $:
$$
8x + 2x - 3 = 10x - 3
$$
✔ Answer: $ 10x - 3 $

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15) $ 12x + 2x - 2 $

$$
14x - 2
$$
✔ Answer: $ 14x - 2 $

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16) $ 13x + 4x - 4 $

$$
17x - 4
$$
✔ Answer: $ 17x - 4 $

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17) $ 2x + (-3)(3x - 3 + x) $

Inside: $ 3x + x - 3 = 4x - 3 $
Multiply: $-3(4x - 3) = -12x + 9 $
Add to $ 2x $:
$$
2x - 12x + 9 = -10x + 9
$$
✔ Answer: $ -10x + 9 $

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18) $ 4x + (-5)(4x - 5 + x) $

Inside: $ 4x + x - 5 = 5x - 5 $
Multiply: $-5(5x - 5) = -25x + 25 $
Add to $ 4x $:
$$
4x - 25x + 25 = -21x + 25
$$
✔ Answer: $ -21x + 25 $

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19) $ 11x + (4x - 4 - x) $

Inside: $ 4x - x - 4 = 3x - 4 $
Add to $ 11x $:
$$
11x + 3x - 4 = 14x - 4
$$
✔ Answer: $ 14x - 4 $

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20) $ 5x + 3x - 2 $

$$
8x - 2
$$
✔ Answer: $ 8x - 2 $

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21) $ 4x - 15x $

$$
(4 - 15)x = -11x
$$
✔ Answer: $ -11x $

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22) $ 21x + 2(5x - 2 + x) $

Inside: $ 5x + x - 2 = 6x - 2 $
Multiply: $ 2(6x - 2) = 12x - 4 $
Add to $ 21x $:
$$
21x + 12x - 4 = 33x - 4
$$
✔ Answer: $ 33x - 4 $

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23) $ 10x + (4x - 2 - x) $

Inside: $ 4x - x - 2 = 3x - 2 $
Add to $ 10x $:
$$
10x + 3x - 2 = 13x - 2
$$
✔ Answer: $ 13x - 2 $

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24) $ 8x + 2x - 3 $

$$
10x - 3
$$
✔ Answer: $ 10x - 3 $

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25) $ 14x - 8x $

$$
6x
$$
✔ Answer: $ 6x $

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26) $ 17x + 3x - 3 $

$$
20x - 3
$$
✔ Answer: $ 20x - 3 $

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27) $ 14x + (-4)(3x - 4 + x) $

Inside: $ 3x + x - 4 = 4x - 4 $
Multiply: $-4(4x - 4) = -16x + 16 $
Add to $ 14x $:
$$
14x - 16x + 16 = -2x + 16
$$
✔ Answer: $ -2x + 16 $

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28) $ 7x + 2x - 3 $

$$
9x - 3
$$
✔ Answer: $ 9x - 3 $

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29) $ 11x + 5x - 4 $

$$
16x - 4
$$
✔ Answer: $ 16x - 4 $

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30) $ 19x + 5x - 2 $

$$
24x - 2
$$
✔ Answer: $ 24x - 2 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 16x - 4 $ |
| 2 | $ 33x - 16 $ |
| 3 | $ -x $ |
| 4 | $ 4x $ |
| 5 | $ x $ |
| 6 | $ -10x + 16 $ |
| 7 | $ 16x - 2 $ |
| 8 | $ 19x - 2 $ |
| 9 | $ 28x - 4 $ |
|10 | $ 19x - 3 $ |
|11 | $ 9x + 9 $ |
|12 | $ 9x + 9 $ |
|13 | $ 4x + 9 $ |
|14 | $ 10x - 3 $ |
|15 | $ 14x - 2 $ |
|16 | $ 17x - 4 $ |
|17 | $ -10x + 9 $ |
|18 | $ -21x + 25 $ |
|19 | $ 14x - 4 $ |
|20 | $ 8x - 2 $ |
|21 | $ -11x $ |
|22 | $ 33x - 4 $ |
|23 | $ 13x - 2 $ |
|24 | $ 10x - 3 $ |
|25 | $ 6x $ |
|26 | $ 20x - 3 $ |
|27 | $ -2x + 16 $ |
|28 | $ 9x - 3 $ |
|29 | $ 16x - 4 $ |
|30 | $ 24x - 2 $ |

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🔍 Key Tips for Combining Like Terms:

- Combine only like terms (same variable and exponent).
- Distribute multiplication over addition/subtraction.
- Watch signs carefully, especially with negative numbers.
- Always simplify inside parentheses first if needed.

Let me know if you'd like this in a printable format or need explanations for any specific problem!