This worksheet provides ten practice problems for students to simplify and order algebraic expressions involving variables like m, y, x, and z.

Here are the step-by-step solutions to simplify each algebraic expression.

1) $(3m - 2) + 2 - m + 3$
* Remove parentheses: $3m - 2 + 2 - m + 3$
* Combine $m$ terms: $3m - m = 2m$
* Combine numbers: $-2 + 2 + 3 = 3$
* Result: $2m + 3$

2) $8 + (-4y + 10) - 3y - 7$
* Remove parentheses: $8 - 4y + 10 - 3y - 7$
* Combine $y$ terms: $-4y - 3y = -7y$
* Combine numbers: $8 + 10 - 7 = 11$
* Result: $-7y + 11$

3) $2(-6 - 2x) + 1 - 3x + 7$
* Distribute the 2 into the parentheses: $-12 - 4x + 1 - 3x + 7$
* Combine $x$ terms: $-4x - 3x = -7x$
* Combine numbers: $-12 + 1 + 7 = -4$
* Result: $-7x - 4$

4) $12 - (20h - 1) - h + 2$
* Distribute the negative sign into the parentheses (change signs inside): $12 - 20h + 1 - h + 2$
* Combine $h$ terms: $-20h - h = -21h$
* Combine numbers: $12 + 1 + 2 = 15$
* Result: $-21h + 15$

5) $7(m - 2) + 5(3 - 2m) + 15$
* Distribute the 7 and the 5: $7m - 14 + 15 - 10m + 15$
* Combine $m$ terms: $7m - 10m = -3m$
* Combine numbers: $-14 + 15 + 15 = 16$
* Result: $-3m + 16$

6) $(5z - 16) + 4z - 13$
* Remove parentheses: $5z - 16 + 4z - 13$
* Combine $z$ terms: $5z + 4z = 9z$
* Combine numbers: $-16 - 13 = -29$
* Result: $9z - 29$

7) $(10y - 4) + (2 - y)(-2) + 3y$
* Multiply $(2 - y)$ by $-2$: This becomes $-4 + 2y$.
* Rewrite expression: $10y - 4 - 4 + 2y + 3y$
* Combine $y$ terms: $10y + 2y + 3y = 15y$
* Combine numbers: $-4 - 4 = -8$
* Result: $15y - 8$

8) $6(3 - 3x) - 2(9 - 3x) - 12$
* Distribute the 6 and the -2: $18 - 18x - 18 + 6x - 12$
* Combine $x$ terms: $-18x + 6x = -12x$
* Combine numbers: $18 - 18 - 12 = -12$
* Result: $-12x - 12$

9) $(-2z - 2) - (2 - 4z) + 5$
* Remove first parentheses: $-2z - 2$
* Distribute negative sign into second parentheses: $-2 + 4z$
* Rewrite expression: $-2z - 2 - 2 + 4z + 5$
* Combine $z$ terms: $-2z + 4z = 2z$
* Combine numbers: $-2 - 2 + 5 = 1$
* Result: $2z + 1$

10) $-4(m - 21) + 4m - 15 + 3m$
* Distribute the -4: $-4m + 84 + 4m - 15 + 3m$
* Combine $m$ terms: $-4m + 4m + 3m = 3m$
* Combine numbers: $84 - 15 = 69$
* Result: $3m + 69$

Final Answer:
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) $3m + 69$