Question

1. $12m + 14n - 7m + 3n + 5$
2. $10m + 12 + 5n + 3m - 3n$
3. $13a + 4b + 3a - 2b$
4. $n + 13 - 5$
5. $19a + 2b + 11a - b$
6. $18c + 4 + 2c$
7. $4q + 18 + 11q$
8. $13a + 9 + 9b + 12a - 7b$
9. $13x + 4 + 2x$
10. $3a + 15 + a$
11. $18z + 10y + 3z - y$
12. $10b + 98 + 16c + 30b - 6c$
13. $p + 23 - 4$
14. $2z + 5 + 3z$
15. $12z + 12y + 13z - y$
16. $4a + 13b - 2a + 2b + 25$
17. $19a + 12b + a - 2b$
18. $12z + 5 + 3z$
19. $y + 56 - 13$
20. $15m + 12n + 5m - 3n$

Answer:

Let's solve each problem by combining like terms:

1) \( 12m + 14n - 7m + 3n + 5 \)

Step1: Combine like terms for \( m \)

\( 12m - 7m = 5m \)

Step2: Combine like terms for \( n \)

\( 14n + 3n = 17n \)

Step3: The constant term is \( 5 \)

So, \( 5m + 17n + 5 \)

2) \( 10m + 12 + 5n + 3m - 3n \)

Step1: Combine like terms for \( m \)

\( 10m + 3m = 13m \)

Step2: Combine like terms for \( n \)

\( 5n - 3n = 2n \)

Step3: The constant term is \( 12 \)

So, \( 13m + 2n + 12 \)

3) \( 13a + 4b + 3a - 2b \)

Step1: Combine like terms for \( a \)

\( 13a + 3a = 16a \)

Step2: Combine like terms for \( b \)

\( 4b - 2b = 2b \)
So, \( 16a + 2b \)

4) \( n + 13 - 5 \)

Step1: Combine constant terms

\( 13 - 5 = 8 \)
So, \( n + 8 \)

5) \( 19a + 2b + 11a - b \)

Step1: Combine like terms for \( a \)

\( 19a + 11a = 30a \)

Step2: Combine like terms for \( b \)

\( 2b - b = b \)
So, \( 30a + b \)

6) \( 18c + 4 + 2c \)

Step1: Combine like terms for \( c \)

\( 18c + 2c = 20c \)

Step2: The constant term is \( 4 \)

So, \( 20c + 4 \)

7) \( 4q + 18 + 11q \)

Step1: Combine like terms for \( q \)

\( 4q + 11q = 15q \)

Step2: The constant term is \( 18 \)

So, \( 15q + 18 \)

8) \( 13a + 9 + 9b + 12a - 7b \)

Step1: Combine like terms for \( a \)

\( 13a + 12a = 25a \)

Step2: Combine like terms for \( b \)

\( 9b - 7b = 2b \)

Step3: The constant term is \( 9 \)

So, \( 25a + 2b + 9 \)

9) \( 13x + 4 + 2x \)

Step1: Combine like terms for \( x \)

\( 13x + 2x = 15x \)

Step2: The constant term is \( 4 \)

So, \( 15x + 4 \)

10) \( 3a + 15 + a \)

Step1: Combine like terms for \( a \)

\( 3a + a = 4a \)

Step2: The constant term is \( 15 \)

So, \( 4a + 15 \)

11) \( 18z + 10y + 3z - y \)

Step1: Combine like terms for \( z \)

\( 18z + 3z = 21z \)

Step2: Combine like terms for \( y \)

\( 10y - y = 9y \)
So, \( 21z + 9y \)

12) \( 10b + 98 + 16c + 30b - 6c \)

Step1: Combine like terms for \( b \)

\( 10b + 30b = 40b \)

Step2: Combine like terms for \( c \)

\( 16c - 6c = 10c \)

Step3: The constant term is \( 98 \)

So, \( 40b + 10c + 98 \)

13) \( p + 23 - 4 \)

Step1: Combine constant terms

\( 23 - 4 = 19 \)
So, \( p + 19 \)

14) \( 2z + 5 + 3z \)

Step1: Combine like terms for \( z \)

\( 2z + 3z = 5z \)

Step2: The constant term is \( 5 \)

So, \( 5z + 5 \)

15) \( 12z + 12y + 13z - y \)

Step1: Combine like terms for \( z \)

\( 12z + 13z = 25z \)

Step2: Combine like terms for \( y \)

\( 12y - y = 11y \)
So, \( 25z + 11y \)

16) \( 4a + 13b - 2a + 2b + 25 \)

Step1: Combine like terms for \( a \)

\( 4a - 2a = 2a \)

Step2: Combine like terms for \( b \)

\( 13b + 2b = 15b \)

Step3: The constant term is \( 25 \)

So, \( 2a + 15b + 25 \)

17) \( 19a + 12b + a - 2b \)

Step1: Combine like terms for \( a \)

\( 19a + a = 20a \)

Step2: Combine like terms for \( b \)

\( 12b - 2b = 10b \)
So, \( 20a + 10b \)

18) \( 12z + 5 + 3z \)

Step1: Combine like terms for \( z \)

\( 12z + 3z = 15z \)

Step2: The constant term is \( 5 \)

So, \( 15z + 5 \)

19) \( y + 56 - 13 \)

Step1: Combine constant terms

\( 56 - 13 = 43 \)
So, \( y + 43 \)

20) \( 15m + 12n + 5m - 3n \)

Step1: Combine like terms for \( m \)

\( 15m + 5m = 20m \)

Step2: Combine like terms for \( n \)

\( 12n - 3n = 9n \)
So, \( 20m + 9n \)

Final Answers:

1. \( \boldsymbol{5m + 17n + 5} \)
2. \( \boldsymbol{13m + 2n + 12} \)
3. \( \boldsymbol{16a + 2b} \)
4. \( \boldsymbol{n + 8} \)
5. \( \boldsymbol{30a + b} \)
6. \( \boldsymbol{20c + 4} \)
7. \( \boldsymbol{15q + 18} \)
8. \( \boldsymbol{25a + 2b + 9} \)
9. \( \boldsymbol{15x + 4} \)
10. \( \boldsymbol{4a + 15} \)
11. \( \boldsymbol{21z + 9y} \)
12. \( \boldsymbol{40b + 10c + 98} \)
13. \( \boldsymbol{p + 19} \)
14. \( \boldsymbol{5z + 5} \)
15. \( \boldsymbol{25z + 11y} \)
16. \( \boldsymbol{2a + 15b + 25} \)
17. \( \boldsymbol{20a + 10b} \)
18. \( \boldsymbol{15z + 5} \)
19. \( \boldsymbol{y + 43} \)
20. \( \boldsymbol{20m + 9n} \)