Pre-Algebra Worksheets | Algebraic Expressions Worksheets - Free Printable

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, I will skip those sections and provide only the final answers to the problems shown in the image.

The worksheet asks to simplify each linear expression by combining like terms. Here are the solutions for problems 1 through 12:

1) $10m - 8n + 2 + 3n$
Combine $-8n$ and $+3n$:
$= 10m - 5n + 2$

2) $3a + 7 + 2(3 + a)$
Distribute the 2: $2 \times 3 = 6$, $2 \times a = 2a$ → $3a + 7 + 6 + 2a$
Combine $3a$ and $2a$: $5a$
Combine $7$ and $6$: $13$
$= 5a + 13$

3) $3(m - 5) + m$
Distribute the 3: $3m - 15 + m$
Combine $3m$ and $m$: $4m$
$= 4m - 15$

4) $2x + 10 - 7y - 3x - 3 - 7$
Combine $2x$ and $-3x$: $-x$
Combine constants $10 - 3 - 7 = 0$
Keep $-7y$
$= -x - 7y$

5) $8c - 4 - 2c + 5$
Combine $8c$ and $-2c$: $6c$
Combine $-4$ and $+5$: $+1$
$= 6c + 1$

6) $-4 + 2x + 3 - 2x$
Combine $2x$ and $-2x$: $0$
Combine $-4$ and $+3$: $-1$
$= -1$

7) $13 + 9(2y + 10)$
Distribute the 9: $9 \times 2y = 18y$, $9 \times 10 = 90$ → $13 + 18y + 90$
Combine $13$ and $90$: $103$
$= 18y + 103$

8) $2d + 17 - 3 - 2d + 4d$
Combine $2d$, $-2d$, and $+4d$: $4d$
Combine $17$ and $-3$: $14$
$= 4d + 14$

9) $12b - 4 - 2b + 10 + 6$
Combine $12b$ and $-2b$: $10b$
Combine constants $-4 + 10 + 6 = 12$
$= 10b + 12$

10) $8(2h + 5 + 3k)$
Distribute the 8: $8 \times 2h = 16h$, $8 \times 5 = 40$, $8 \times 3k = 24k$
$= 16h + 40 + 24k$
(Rearranged as $16h + 24k + 40$ if preferred, but order doesn’t matter)

11) $4(2g + 2) - 3$
Distribute the 4: $8g + 8 - 3$
Combine $8$ and $-3$: $5$
$= 8g + 5$

12) $-4 + 8p - 6p - 5 + 2(p)$
First, simplify $2(p)$ to $2p$
Now: $-4 + 8p - 6p - 5 + 2p$
Combine $8p - 6p + 2p = 4p$
Combine $-4 - 5 = -9$
$= 4p - 9$

Final Answer:
1) $10m - 5n + 2$
2) $5a + 13$
3) $4m - 15$
4) $-x - 7y$
5) $6c + 1$
6) $-1$
7) $18y + 103$
8) $4d + 14$
9) $10b + 12$
10) $16h + 24k + 40$
11) $8g + 5$
12) $4p - 9$