Worksheet for simplifying variable expressions with algebraic problems.

Let's solve each of the algebraic expressions step by step, simplifying and ordering them. We'll combine like terms and follow the order of operations.

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1) (3m - 2) + 2 - m + 3

Step-by-step:
- Remove parentheses:
$ 3m - 2 + 2 - m + 3 $
- Combine like terms:
- $ 3m - m = 2m $
- $ -2 + 2 + 3 = 3 $
- Final answer:
$ \boxed{2m + 3} $

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2) 8 + (-4y + 10) - 3y - 7

Step-by-step:
- Remove parentheses:
$ 8 - 4y + 10 - 3y - 7 $
- Combine like terms:
- $ -4y - 3y = -7y $
- $ 8 + 10 - 7 = 11 $
- Final answer:
$ \boxed{-7y + 11} $

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3) 2(-6 - 2x) + 1 - 3x + 7

Step-by-step:
- Distribute the 2:
$ 2 \cdot (-6) = -12 $, $ 2 \cdot (-2x) = -4x $
So: $ -12 - 4x + 1 - 3x + 7 $
- Combine like terms:
- $ -4x - 3x = -7x $
- $ -12 + 1 + 7 = -4 $
- Final answer:
$ \boxed{-7x - 4} $

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4) 12 - (20h - 1) - h + 2

Step-by-step:
- Distribute the negative sign:
$ 12 - 20h + 1 - h + 2 $
- Combine like terms:
- $ -20h - h = -21h $
- $ 12 + 1 + 2 = 15 $
- Final answer:
$ \boxed{-21h + 15} $

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5) 7(m - 2) + 5(3 - 2m) + 15

Step-by-step:
- Distribute:
- $ 7m - 14 $
- $ 5 \cdot 3 = 15 $, $ 5 \cdot (-2m) = -10m $
So: $ 7m - 14 + 15 - 10m + 15 $
- Combine like terms:
- $ 7m - 10m = -3m $
- $ -14 + 15 + 15 = 16 $
- Final answer:
$ \boxed{-3m + 16} $

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6) (5z - 16) + 4z - 13

Step-by-step:
- Remove parentheses:
$ 5z - 16 + 4z - 13 $
- Combine like terms:
- $ 5z + 4z = 9z $
- $ -16 - 13 = -29 $
- Final answer:
$ \boxed{9z - 29} $

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7) (10y - 4) + (2 - y)(-2) + 3y

Step-by-step:
- First, simplify $ (2 - y)(-2) $:
- Distribute: $ 2 \cdot (-2) = -4 $, $ -y \cdot (-2) = 2y $
- So: $ -4 + 2y $
- Now plug back in:
$ 10y - 4 + (-4 + 2y) + 3y $
- Combine all:
- $ 10y + 2y + 3y = 15y $
- $ -4 - 4 = -8 $
- Final answer:
$ \boxed{15y - 8} $

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8) 6(3 - 3x) - 2(9 - 3x) - 12

Step-by-step:
- Distribute:
- $ 6 \cdot 3 = 18 $, $ 6 \cdot (-3x) = -18x $
- $ -2 \cdot 9 = -18 $, $ -2 \cdot (-3x) = +6x $
- So: $ 18 - 18x - 18 + 6x - 12 $
- Combine like terms:
- $ -18x + 6x = -12x $
- $ 18 - 18 - 12 = -12 $
- Final answer:
$ \boxed{-12x - 12} $

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9) (-2z - 2) - (2 - 4z) + 5

Step-by-step:
- Distribute the negative sign to the second group:
$ -2z - 2 - 2 + 4z + 5 $
- Combine like terms:
- $ -2z + 4z = 2z $
- $ -2 - 2 + 5 = 1 $
- Final answer:
$ \boxed{2z + 1} $

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10) -4(m - 21) + 4m - 15 + 3m

Step-by-step:
- Distribute:
$ -4m + 84 $
- Now add the rest:
$ -4m + 84 + 4m - 15 + 3m $
- Combine like terms:
- $ -4m + 4m + 3m = 3m $
- $ 84 - 15 = 69 $
- Final answer:
$ \boxed{3m + 69} $

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✔ Final Answers:

1) $ 2m + 3 $
2) $ -7y + 11 $
3) $ -7x - 4 $
4) $ -21h + 15 $
5) $ -3m + 16 $
6) $ 9z - 29 $
7) $ 15y - 8 $
8) $ -12x - 12 $
9) $ 2z + 1 $
10) $ 3m + 69 $

Let me know if you'd like these explained in a different way or formatted for printing!