PROBLEM SET 19
Terminology
1.
A quantity’s ADDITIVE INVERSE is just itself with the opposite sign.
Examples:
2.
The additive inverse of -8 is 8
The additive inverse of 15x is -15x
The additive inverse of 6 x 11 p is 6 x 11 p
SUBTRATION is just adding the opposite.
Examples:
(We added the opposite of 9, which was -9)
(We added the opposite of -25, which was 25)
12 9 12 9 3
13
25 13 25 38
7
4
7 4
7 p 8p
7p
3
(We added the opposite of -4, which was 4)
15 p (We added the opposite of 8p, which was -8p)
8p
1
Also, on more complicated ones, you can always think of a subtraction sign as
(adding a “negative 1 times”)
Simplify:
5x
1.
9 7x
5x
1
9 7x
5x
9 7x
5x
1
9 7x
5x
9
2x
2.
7x
Then, we just distribute and
simplify:
9
4x 9
9
1 4x 9
3.
9
1 4x
19
1 4x
9
4x 9
4x
9
3 p 5w 7 p
That first negative can be written as a 1
19
And then those subtraction signs can be changed to
9
4p w
3p
1 5w
3p
5w
7p
1 4p
3p
5w
7p
4p w
8p
See how the subtraction sign
1 ?
turned into
1 7p
1 4p
1 w
w
4w
Page 37
1
Problem Set 19 Homework
A.
Complete the table.
Quantity
The Quantity’s additive inverse
13
5m
5x
7y
3ab 11w
3 9x
y
2t 3w
B.
Change all subtractions to additive form. Do not simplify.
1.
5 7
6.
4
2.
4 6
7.
5y
3.
C.
8p
5 3
8.
4.
3
5.
8x 5x
4
2
5
3x 7
8m 3
3 2m
9.
3d 5 2 5d 7
10.
3 76 2
1
Write in additive form and then simplify.
1.
10 3
5.
2.
12 18
6.
7x
3.
2m 8m
7.
3 5 7
4.
13
8.
7
Page 38
5p
31k
3p
p
3x
9x
2
30k
8m
PROBLEM SETS 20 & 21
These sections are similar to 19, just a little more involved. Problem set 20 asks you to just simplify and
Problem set 21 asks you to simplify AND THEN factor. Thus, it’s like two problems in one.
Examples:
Simplify:
1.
5
3p
18 p
15
2.
Answer:
5
1 3p
1 18 p
1
3x 9
Answer:
1 3x
15
5 3 p 18 p 15
10 15 p
6 x 10
19
1 6x
1 3x
9
1 6x
3x 9
6 x 10
9 x 19
Simplify AND THEN factor:
3.
5 4x 5 4x 6
Answer:
5 4x
1 5 4x
16
5 4x
5 4x
6
5 4x
20 x 30
Note that right here, we have simplified it.
5 16 x 30
80 x 150
And the LAST step is factoring.
10 8 x 15
4.
3
5 x 4 11x 2
Answer:
3 1 5x
3
1 5x
3
1 6x
3 6x 6
9 12 x
1 4
4
1 11x
11x
6
19
2
1 2
1 9
19
12 x
12 x
9 12 x
6 18 x
6
1 3x
Page 39
1 12 x
1 10
10
Problem set 20 Homework
Simplify.
1.
6 4
2.
12
3.
4x
4.
9 4
5.
5m
16.
9de 6xy
7
17.
2 3m
2x
18.
10
x
3
19. a
2
8 0
21. 5
7.
2 7
22.
8.
3 10
23.
10.
8p 5
7p
7
12.
6gh 3g
8gh
26.
27.
3g
13. 0 8 9
14.
5ab
15. 3ab
3x 1
6ab
5ab
6a
x 1
5
5 3 2 6
11
1
3v 5 v 1
6 7
a 2b 7c
a 5b
28. 2 3my
3b
7n 3m
1 b a
25. 2x 1 5y
11. 2a 7 5a
de
2 5x
24. 3 5
3
17y 17y
4g
8n
20. 2 x 1
3m
6.
9.
4
xy
4
1
7y 3 2x
b a c
4a 9b
2
5 my
29. 5z 3z 16 23
3b
30.
7ab
Page 40
12x 9t
3x 5t
c 2a 4b
Problem Set 21 Homework
Simplify, then factor completely, if possible.
1.
2 h 3
2.
9 3 x 2
17.
2 2 3m 5 m
3.
2
18.
4 3 3 2 x 4
4.
7 2 4
5.
s 3
2
3u
7.
21xy x 3
8.
4
20.
3u 5u
3m
6x
12
53
22.
24.
4 t 2
4
12. 10a
3a 2
13. 4 2
3
14.
3
y 2
15.
2
2
2
3 A 3a
4
2
3
2
4
6a
x
y
u 11
5
26.
25 3
5
6
7
3a 4 5b
3y
29.
29 71
30.
19m 7m
Page 41
2
2A 5a
2 3 x 4y
28. 14 2
5
1
2
2
2
5
25. 7 5u 3
27.
5
3
3
3 2 4x 3
23. 2 3 4
5x 7
2k 4
3 6k
y 2 3 2y
21. 4 3 6
4u
2 x
4
10. 2 t 3
11.
19.
14
7 3 2x 1
6.
9.
16. 4 2 k 2
4
3
2a 6ab
2
3
20
3m 21m
2
5