Matemáticas

8

SOLUCIONES A LOS EJERCICIOS
DE LA UNIDAD
Pág. 1

PÁGINA 159
EJERCICIOS DE LA UNIDAD
Primeras ecuaciones

1

4x – 1 = 7
4x = 8 → x = 2

2

2 – 5x = 12
–5x = 10 → x = –2

3

4 – 3x = 4
–3x = 0 → x = 0

4

5x + 3 = 3
5x = 0 → x = 0

5

11 = 5 + 4x
4x = 6 → x = 3
2

6

0 = 21 – 7x
7x = 21 → x = 3

7

13x – 5 – 6x = 9
7x = 14 → x = 2

8

6 – x = 3 –4x
3 = –3x → x = –1

9

2x – 5 + x = 1 + 3x – 6
3x – 5 = 3x – 5
0=0
Cualquier solución es válida.

Unidad 8. Ecuaciones

8

SOLUCIONES A LOS EJERCICIOS
DE LA UNIDAD
Pág. 2

10

1 – 8x + 5 = 11 – 3x
6 – 8x = 11 – 3x → 5x = –5 → x = –1

11

7x + 2x = 2x + 1 + 6x
9x = 8x + 1 → x = 1

12

2x + 8 – 9x = 7 + 2x – 2
–7x + 8 = 2x + 5 → 9x = –3 → x = – 1
3

13

10 – 15x+ 2 = 10x + 5 – 11x
12 – 15x = 5 – x → 14x = 7 → x = 1
2

14

3 – (1 – 6x) = 2 + 4x
2 + 6x = 2 + 4x → x = 0

15

3(x – 1) – 4x = 5 – (x + 7)
3x – 3 – 4x = 5 – x – 7 → –x – 3 = –2 – x → –3 = –2
No tiene solución.

16

2x – 2(x – 1) + 5 = 4 – 3(x + 1)
2x – 2x + 2 + 5 = 4 – 3x – 3 → 7 = 1 – 3x → –3x = 6 → x = – 6 = –2
3

17

5(2x – 3) – 8x = 14x – 3(4x + 5)
10x – 15 – 8x = 14x– 12x – 15 → 2x = 2x → 0 = 0
Infinitas soluciones.

18

3(x – 2) – 5 (2x – 1) – 2(3x + 4) + 10 = 0
(
)
(
)
(
)
3x – 6 – 10x + 5 – 6x – 8 + 10 = 0 → –13x + 1 = 0 → x = 1
13

Unidad 8. Ecuaciones

8

SOLUCIONES A LOS EJERCICIOS
DE LA UNIDAD
Pág. 3

19

5x – 2(3x – 4) = 25 – 3(5x + 1)
5x – 6x + 8 = 25 – 15x – 3 → –x + 8 = 22 – 15x → 14x = 14 → x = 1

20

3(4x – 1) –2(5x – 3) = 11 – 2x
12x – 3 – 10x + 6 = 11 – 2x → 2x + 3 = 11 – 2x → 4x = 8 → x = 2

Ecuaciones de primer grado con denominadores

21
21

5 – x = 3x – 16
2
10 – x = 6x – 32 → 7x = 42 → x = 6

22
22

x – x = 2x – 2
3
3
3x – x = 6x – 2 → 4x = 2 → x = 1
2

23
23

x – x = 4
2
6 3
3x – x = 8 → 2x = 8 → x = 4

24
24

x – x = 3
5 8 4
8x – 5x = 30 → 3x = 30 → x = 10

2525

x – 1 = 5x – 3
2
8
4
8x – 4 = 5x – 6 → 3x = –2 → x = – 2
3

26
26

x + 1 – x = 3x + 8
2 5 6 10 15
15x + 6 – 5x = 9x + 16 → 10x + 6 = 9x + 16 → x = 10

27
27

x – 1 + x + 1 = x – 1
3 2 6 4 2 4
4x – 6 + 2x + 3 = 6x – 3 → 6x – 3 = 6x – 3 → 0 = 0 → Infinitas soluciones

Unidad 8. Ecuaciones

8

SOLUCIONES A LOS EJERCICIOS
DE LA UNIDAD
Pág. 4

28
28

x – x + x =2x + 7
2 3 5 15
15x – 10x + 6x = 4x + 210 → 7x = 210 → x = 30

29
29

3x – 1 = 5x – 4
2
3
9x – 3 = 10x – 8 → x = 5

30
30

1 = 5
x + 1 2x – 4
2x – 4 = 5x + 5 → 3x = –9 → x = –3

32
32

1 + x – 1 = 3x
2
2 + x – 1 = 6x → x + 1 = 6x → 5x = 1 → x = 1
5

33
33

x + x–2 =1
2
4
2x + x – 2 = 4 → 3x = 6 → x = 2

34
34

1– x+2 =x
3
3 – x – 2 = 3x → 4x = 1 → x = 1
435
35

x – x+2 = x
3
9
3
3x – x – 2 = 3x → x = –2

36
36

x– x–5 =4
2
2x – x + 5 = 8 → x = 3

PÁGINA 160
37
37

x–7 + x–1 =x–5
4
3
3x – 21 + 4x – 4 = 12x – 60 → 7x – 25 = 12x – 60 → 5x = 35 → x = 7

Unidad 8. Ecuaciones

SOLUCIONES A LOS EJERCICIOS
DE LA UNIDAD

8

Pág. 5

3 – 2x = x – 3x – 1
5
2

38
38

30 – 4x = 10x – 15x + 5 → 25 = –x → x = –25
x–1 –x+1 =1
2
3

39
39

3x – 3 – 2x – 2 = 6 → x – 5 = 6 → x = 11
x–1 – 1–x = x–1
5
6
4

40
40

12x – 12 – 10 + 10x = 15x – 15 → 22x – 22 = 15x – 15 → 7x = 7 → x = 1
3x – 2 – 2x – 1 = 5x – 7
5
3
15

41
41

9x – 6 – 10x + 5 = 5x – 7 → –x – 1 = 5x – 7 → 6x = 6 → x = 1
4 (1 – 2x) + 5 (2x – 1) = 7 (x – 2)
3
4
12

42
42

16 (1 – 2x) + 15 (2x – 1) = 7(x – 2) → 16 – 32x + 30x– 15 = 7x – 14 →
→ 1 – 2x = 7x – 14 → 9x = 15 → x = 15
9
2 (x + 1) – 1 – x = x + 3
3
5
10

43
43

20 (x + 1) – 6 + 6x = 30x + 9 → 20x + 20 – 6 + 6x = 30x + 9 →
→ 26x + 14 = 30x + 9 → 4x = 5 → x = 5
4
44
44

(

)

2 5x – x – 4 = 4x
3
10x – 2x – 8 = 4x → 30x – 2x + 8 = 12x → 16x = –8 → x = – 1
3
2

(

)

2 1 – x+1 = 5
3 2
4
6

45
45
2
3

( 2 – 4x – 1 ) = 5...