1. No category

5
Soluciones a las actividades de cada epígrafe
PÁGINA 97
Pág. 1
1 Resuelve las siguientes ecuaciones:
a) 3x – x = – 3x + 9
15
3 5
c) x + x – 3 + 2x + 2 = x – 2
2
8
16
2
e) 3x – x + 3 = 13
4
g) x – 2(x + 2) = x – 3
2
7
4
2
2
i) (1 + x) = 2x + 4 + x + 1
5
5 5
25
k) x + 9(5 + x) = 9 – x
5
m) (x – 3)(x + 3) = 3(x – 1) + x 2
2
a) 3x – x = – 3x + 9
15
3 5
3x – 15x = –15x + 27
3x – 15x + 15x = 27
3x = 27
x=9
b) x + x – 4x = 11 – x
3 9 27 27 9
9x + 3x – 4x = 11 – 3x
9x + 3x – 4x + 3x = 11
11x = 11
x=1
c) x + x – 3 + 2x + 2 = x – 2
2
8
16
2
8x + 2(x – 3) + 2x + 2 = 8(x – 2)
8x + 2x – 6 + 2x + 2 = 8x – 16
8x + 2x + 2x – 8x = –16 + 6 – 2
4x = –12
x = –3
Unidad 5. Ecuaciones
b) x + x – 4x = 11 – x
3 9 27 27 9
d) 13 + x – 5x = 10 + x + 1 – 12x
20
2
5
10
f) 4 – x + 2 = x – 4
4
h) 1 – x – x + x + 7 = 2 – 3x
25
6
9
5 15
j) x – 4 + 9 – x – 2x – 7 + 5 = x – 8
8
12
24
2
l) (2x – 1)(2x + 1) = 3(4x + 1) – x
4
12
n) x – 7 + 25(x – 2) = 5x + 35 + 5 (x – 7)
4
3
4
2
5
Soluciones a las actividades de cada epígrafe
d) 13 + x – 5x = 10 + x + 1 – 12x
20
2
5
10
13 + x – 50x = 4(10 + x) + 2(1 – 12x)
13 + x – 50x = 40 + 4x + 2 – 24x
x – 50x – 4x + 24x = 40 + 2 – 13
–29x = 29
x = –1
e) 3x – x + 3 = 13
4
12x – (x + 3) = 52
12x – x – 3 = 52
12x – x = 52 + 3
11x = 55
x=5
f) 4 – x + 2 = x – 4
4
16 – (x + 2) = 4(x – 4)
16 – x – 2 = 4x – 16
–x – 4x = –16 – 16 + 2
–5x = –30
x=6
g) x – 2(x + 2) = x – 3
2
7
4
14x – 8(x + 2) = 7(x – 3)
14x – 8x – 16 = 7x – 21
14x – 8x – 7x = –21 + 16
–x = –5
x=5
h) 1 – x – x + x + 7 = 2 – 3x
25
6
9
5 15
18(1 – x) – 75x + 50(x + 7) = 180 – 90x
18 – 18x – 75x + 50x + 350 = 180 – 90x
–18x – 75x + 50x + 90x = 180 – 18 – 350
47x = –188
x = –4
Unidad 5. Ecuaciones
Pág. 2
5
Soluciones a las actividades de cada epígrafe
2
2
i) (1 + x) = 2x + 4 + x + 1
5
5 5
25
5(1 + x)2 = 2x + 4 + 5x 2 + 5
5(1 + 2x + x 2) = 2x + 5x 2 + 9
5 + 10x + 5x 2 = 2x + 5x 2 + 9
10x + 5x 2 – 2x – 5x 2 = 9 – 5
8x = 4 8 x = 1
2
j) x – 4 + 9 – x – 2x – 7 + 5 = x – 8
8
12
24
3(x – 4) + 2(9 – x) – (2x – 7) + 120 = 24(x – 8)
3x – 12 + 18 – 2x – 2x + 7 + 120 = 24x – 192
3x – 2x – 2x – 24x = –192 + 12 – 18 – 7 – 120
–25x = –325
x = 13
k) x + 9(5 + x) = 9 – x
5
5x + 9(5 + x) = 5(9 – x)
5x + 45 + 9x = 45 – 5x
5x + 9x + 5x = 45 – 45
19x = 0
x=0
2
l) (2x – 1)(2x + 1) = 3(4x + 1) – x
4
12
3(4x 2 – 1) = 3(4x 2 + 1) – 12x
12x 2 – 3 = 12x 2 + 3 – 12x
12x 2 – 12x 2 + 12x = 3 + 3
12x = 6
x= 1
2
m) (x – 3)(x + 3) = 3(x – 1) + x 2
2
2(x 2 – 9) = 3(x – 1) + 2x 2
2x 2 – 18 = 3x – 3 + 2x 2
2x 2 – 3x – 2x 2 = –3 + 18
–3x = 15
x = –5
Unidad 5. Ecuaciones
Pág. 3
5
Soluciones a las actividades de cada epígrafe
n) x – 7 + 25(x – 2) = 5x + 35 + 5 (x – 7)
4
3
4
2
3(x – 7) + 100(x – 2) = 3(5x + 35) + 30(x – 7)
3x – 21 + 100x – 200 = 15x + 105 + 30x – 210
3x + 100x – 15x – 30x = 105 – 210 + 21 + 200
58x = 116
x=2
Unidad 5. Ecuaciones
Pág. 4