- Ejercicio 9
ejercicios, reducimos todos los términos positivos y los términos
negativos, después realizamos la suma algebraica de ambos.
-
9 a – 3 a + 5 a = ( 9 a + 5 a
)
– 3 a = 14 a – 3 a = 11 a -
– 8 x + 9 x – x = ( – 8 x – x
)
+ 9 x ) = – 9 x + 9 x = 0 -
12 m n – 23 m n – 5 m n = ( – 23 m n – 5 m n
)
+ 12 m n = – 28 m n + 12 m n = – 16 m n -
– x + 19 x – 18 x = ( – x – 18 x
)
+ 19 x = – 19 x + 19 x = 0 -
19 m – 10 m + 6 m = ( 19 m + 6 m
)
– 10 m = 15 m – 10 m = 5 m -
– 11 a b – 15 a b + 26 a b = ( – 11 a b – 15 a b
)
+ 26 a b = – 26 a b + 26 a b = 0 -
– 5
a
x
+ 9 a
x
– 35 a
x
= ( – 5 a
x
– 35 a
x
)
+ 9 a
x
= – 40 a
x
+ 9 a
x
= – 31 a
x
-
– 24
a
x + 2
– 15 a
x + 2
+ 39 a
x + 2
= ( – 24 a
x + 2
– 15 a
x + 2
)
+ 39 a
x + 2
= – 39 a
x + 2
+ 39 a
x + 2
= 0 -
2
3
y +
1
3
y – y = (
2
3
y +
1
3
y
)
– y = (
2 y + y
3
)
– y = y – y = 0 -
–
3
5
m +
1
4
m –
1
2
m = ( –
3
5
m –
1
2
m
)
+
1
4
m = (
– 6 m – 5 m
10
)
+
1
4
m = –
11
10
m +
1
4
m =
– 22 m + 5 m
20
= –
17 m
20
-
3
8
a
2
b +
1
4
a
2
b –
a
2
b = (
3
8
a
2
b +
1
4
a
2
b
)
–
a
2
b = (
3
a
2
b + 2
a
2
b
8
)
–
a
2
b =
5
8
a
2
b –
a
2
b =
5
a
2
b – 8
a
2
b
8
= –
3
a
2
b
8
-
– a + 8 a + 9 a – 15 a = ( – a – 15 a
)
+ ( 8 a + 9 a
)
= – 16 a + 17 a = a -
7 a b – 11 a b + 20 a b – 31 a b = ( – 11 a b – 31 a b
)
+ ( 7 a b + 20 a b
)
= – 42 a b + 27 a b = – 15 a b -
25
x
2
– 50 x
2
+ 11 x
2
+ 4 x
2
= ( 25
x
2
+ 11 x
2
+ 4 x
2
)
– 50 x
2
= 40 x
2
– 50 x
2
= – 10 x
2
-
– x y – 8 x y + 19 x y + 40 x y = ( – x y – 8 x y
)
+ ( 19 x y + 40 x y
)
= – 9 x y + 59 x y = 50 x y -
7 a b + 21 a b – a b – 80 a b = ( – a b – 80 a b
)
+ ( 7 a b + 21 a b
)
= – 81 a b + 28 a b = – 53 a b -
– 25 x
y
2
+ 11 x
y
2
+ 60 x
y
2
– 82 x
y
2
= ( – 25 x
y
2
– 82 x
y
2
)
+ ( 11 x
y
2
+ 60 x
y
2
)
= – 107 x
y
2
+ 71 x
y
2
= – 36 x
y
2
-
– 72 a x + 87 a x – 101 a x + 243 a x = ( – 72 a x – 101 a x
)
+ ( 87 a x + 243 a x
)
= – 173 a x + 330 a x = – 157 a x -
– 82 b x – 71 b x – 53 b x + 206 b x = ( – 82 b x – 71 b x – 53 b x
)
+ 206 b x = – 206 b x + 206 b x = 0 -
105
a
3
– 464 a
3
+ 58 a
3
+ 301 a
3
= ( 105 a
3
+ 58 a
3
+ 301 a
3
)
– 464 a
3
= 464 a
3
– 464 a
3
= 0 -
1
2
x –
1
3
x +
1
4
x –
1
5
x = ( –
1
3
x –
1
5
x
)
+ (
1
2
x +
1
4
x
)
=
– 5 x – 3 x
15
+
2 x + x
4
= –
8
15
x +
3
4
x =
– 32 x + 45 x
60
=
13 x
60
-
1
3
y –
1
3
y +
1
6
y –
1
12
y = ( –
1
3
y –
1
12
y
)
+ (
1
3
y +
1
6
y
)
=
– 4 y – y
12
+
2 y + y
6
= –
5
12
y +
y
2
=
– 5 y + 6 y
12
=
y
12
-
3
5
a
2
b –
1
6
a
2
b +
1
3
a
2
b –
a
2
b = ( –
1
6
a
2
b –
a
2
b
)
+ (
3
5
a
2
b +
1
3
a
2
b
)
=
–
a
2
b – 6
a
2
b
6
+
9
a
2
b + 5
a
2
b
15
= –
7
a
2
b
6
+
14
a
2
b
15
=
– 35
a
2
b + 28
a
2
b
30
= –
7
a
2
b
30
-
–
5
6
a
b
2
–
1
6
a
b
2
+ a
b
2
–
3
8
a
b
2
= ( –
5
6
a
b
2
–
1
6
a
b
2
–
3
8
a
b
2
)
+ a
b
2
=
– 20 a
b
2
– 4 a
b
2
– 9 a
b
2
24
+ a
b
2
=
– 11 a
b
2
8
+ a
b
2
=
– 11 a
b
2
+ 8 a
b
2
8
= –
3 a
b
2
8
-
– a + 8 a – 11 a + 15 a – 75 a = ( – a – 11 a – 75 a
)
+ ( 8 a + 15 a
)
= – 87 a + 23 a = – 64 a -
– 7 c + 21 c + 14 c – 30 c + 82 c = ( – 7 c – 30 c
)
+ ( 21 c + 14 c + 82 c
)
= – 37 c + 117 c = 80 c -
– m n + 14 m n – 31 m n – m n + 20 m n = ( – m n – 31 m n – m n
)
+ ( 14 m n + 20 m n
)
= – 33 m n + 34 m n = m n -
a
2
y – 7 a
2
y – 93 a
2
y + 51 a
2
y + 48 a
2
y = ( – 7 a
2
y – 93 a
2
y
)
+ ( a
2
y + 51 a
2
y + 48 a
2
y
)
= – 100 a
2
y + 100 a
2
y = 0 -
– a + a – a + a – 3 a + 6 a = ( – a – a – 3 a
)
+ ( a + a + 6 a
)
= – 5 a + 8 a = 3 a -
1
2
x +
2
3
x –
7
6
x +
1
2
x – x = ( –
7
6
x – x
)
+ (
1
2
x +
2
3
x +
1
2
x
)
=
– 7 x – 6 x
6
+
3 x + 4 x + 3 x
6
= –
13 x
6
+
10 x
6
=
– 13 x + 10 x
6
= –
3 x
6
= –
x
2
-
– 2 x +
3
4
x +
1
4
x + x –
5
6
x = ( – 2 x –
5
6
x
)
+ (
3
4
x +
1
4
x + x
)
=
– 12 x – 5 x
6
+
3 x + x + 4 x
4
= –
17 x
6
+ 2 x =
– 17 x + 12 x
6
= –
5 x
6
-
7
a
x
– 30 a
x
– 41 a
x
– 9 a
x
+ 73 a
x
= ( – 30 a
x
– 41 a
x
– 9 a
x
)
+ ( 7 a
x
+ 73 a
x
)
= – 80 a
x
+ 80 a
x
= 0 -
–
a
x + 1
+ 7 a
x + 1
– 11 a
x + 1
– 20 a
x + 1
+ 26 a
x + 1
= ( – a
x + 1
– 11 a
x + 1
– 20 a
x + 1
)
+ ( 7 a
x + 1
+ 26 a
x + 1
)
= – 32 a
x + 1
+ 33 a
x + 1
= a
x + 1
-
a + 6 a – 20 a + 150 a – 80 a + 31 a = ( – 20 a – 80 a
)
+ ( a + 6 a + 150 a + 31 a
)
= – 100 a + 188 a = 88 a -
– 9 b – 11 b – 17 b – 81 b – b + 110 b = ( – 9 b – 11 b – 17 b – 81 b – b
)
+ 110 b = – 119 b + 110 b = – 9 b -
–
a
2
b + 15
a
2
b +
a
2
b – 85
a
2
b – 131
a
2
b + 39
a
2
b = ( –
a
2
b – 85
a
2
b – 131
a
2
b
)
+ ( 15
a
2
b +
a
2
b + 39
a
2
b
)
= – 217
a
2
b + 55
a
2
b = – 162
a
2
b -
84
m
2
x – 501 m
2
x – 604 m
2
x – 715 m
2
x + 231 m
2
x + 165 m
2
x = ( – 501 m
2
x – 604 m
2
x – 715 m
2
x
)
+ ( 84 m
2
x + 231 m
2
x + 165 m
2
x
)
= – 1820 m
2
x + 480 m
2
x = – 1340 m
2
x -
5
6
a
3
b
2
+
2
3
a
3
b
2
–
1
4
a
3
b
2
–
5
8
a
3
b
2
+ 4 a
3
b
2
= ( –
1
4
a
3
b
2
–
5
8
a
3
b
2
)
+ (
5
6
a
3
b
2
+
2
3
a
3
b
2
+ 4 a
3
b
2
)
=
– 7
a
3
b
2
8
+
33
a
3
b
2
6
=
– 21
a
3
b
2
+ 132 a
3
b
2
24
=
37
a
3
b
2
8
-
40 a – 81 a + 130 a + 41 a – 83 a – 91 a + 16 a = ( – 81 a – 83 a – 91 a
)
+ ( 40 a + 130 a + 41 a + 16 a
)
= – 255 a + 227 a = – 28 a -
– 21 a b + 52 a b – 60 a b + 84 a b – 31 a b – a b – 23 a b = ( – 21 a b – 60 a b – 31 a b – a b – 23 a b
)
+ ( 52 a b + 84 a b
)
= –
136 a b
+
136 a b
= 0