resuelve las ecuasiones a) 2x + 7= x + 15 b) -4 + x = -12 c) 1 + 3x = 2x + 3 d) x + 2x - 5 = -4x + 6 e) 5x + 5x + 13 = 65x - 36 F) 5x + 6 = 10x + 5 g)9y + 11 = -10 + 12y h) 8x + 4 + 3x = 7x + x - 14 i) 5y + 6y - 81 = 7y + 102 + 65y J) 8x - 15x - 30x - 51x = 53x + 31x - 172 k)3x + 101 - 4x - 33 = 108 - 16x - 100 L)16 + 7x - 5 + x = 11x - 3 - x PLISSS AYUDAAAA
Respuestas
- Ecuaciones:
a) Solución:
2x + 7 = x + 15
2x - x = 15 - 7
x = 8
Comprobamos:
2x + 7 = x + 15
2 . 8 + 7 = 8 + 15
16 + 7 = 23
23 = 23
b) Solución:
-4 + x = -12
x = -12 + 4
x = -8
Comprobamos:
- 4 + x = -12
-4 + (-8) = -12
-4 - 8 = -12
-12 = -12
c) Solución:
1 + 3x = 2x + 3
3x - 2x = 3 - 1
x = 2
Comprobamos:
1 + 3x = 2x + 3
1 + 3 . 2 = 2 . 2 + 3
1 + 6 = 4 + 3
7 = 7
d) Solución:
x + 2x - 5 = -4x + 6
x + 2x + 4x = 6 + 5
7x = 11
x = 11/7
Comprobamos:
x + 2x - 5 = - 4x + 6
11/7 + 2 . 11/7 - 5/1 = -4 . 11/7 + 6
11/7 + 2.11/1.7 - 5/1 = -4.11/1.7 + 6/1
11/7 + 22/7 - 5/1 = -44/7 + 6/1
7:7.11+7:7.22-7:1.5/7 = 7:7.(-44)+7:1.6/7
11+22-35/7 = -44+42/7
-2/7 = -2/7
e) Solución:
5x + 5x + 13 = 65x - 36
10x + 13 = 65x - 36
10x - 65x = -36 - 13
-55x = -49
x = -49/-55
Comprobamos:
5x + 5x + 13 = 65x - 36
5 . -49/-55 + 5 . -49/-55 + 13 = 65 . -49/-55 - 36
5.(-49)/1.(-55) + 5.(-49)/1.(-55) + 13 = 65.(-49)/1.(-55) - 36
-245/-55 + -245/-55 + 13 = -3185/-55 - 36
245/55 + 245/55 + 13/1 = 3185/55 - 36/1
55:55.245+55:55.245+55:1.13/55 = 55:55.3185-55:1.36/55
245+245+715/55 = 3185-1980/55
1205/55 =1205/55
f) Solución:
5x + 6 = 10x + 5
5x - 10x = 5 - 6
-5x = -1
x = -1/-5
x = 1/5
Comprobamos:
5x + 6 = 10x + 5
5 . 1/5 + 6 = 10 . 1/5 + 5
5.1/1.5 + 6 = 10.1/1.5 + 5
5/5 + 6 = 10/5 + 5
1 + 6 = 2 + 5
7 = 7
g) Solución:
9y + 11 = -10 + 12y
9y - 12y = -10 - 11
-3y = -21
y = -21 : -3
y = 7
Comprobamos:
9y + 11 = -10 + 12y
9 . 7 + 11 = -10 + 12 . 7
63 + 11 = -10 + 84
74 = 74
h) Solución:
8x + 4 + 3x = 7x + x - 14
8x + 3x - 7x - x = - 14 - 4
3x = -18
x = -18/3
x = -6
Comprobamos:
8x + 4 + 3x = 7x + x - 14
8 . (-6) + 4 + 3 . (-6) = 7 . (-6) + (-6) - 14
-48 + 4 + (-18) = -42 - 6 - 14
-62 = -62
i) Solución:
5y + 6y - 81 = 7y + 102 + 65y
5y + 6y - 7y - 65y = 102 +81
-61y = 183
y = 183 : -61
y = -3
Comprobamos:
5y + 6y - 81 = 7y + 102 + 65y
5 . (-3) + 6 . (-3) - 81 = 7 . (-3) + 102 + 65 . (-3)
-15 + (-18) - 81 = -21 + 102 + (-195)
-15 - 18 - 81 = -21 + 102 - 195
-114 = -114
j) Solución:
8x - 15x - 30x - 51x = 53x + 31x - 172
8x - 15x - 30x - 51x - 53x - 31x = -172
-172x = -172
x = -172/-172
x = 1
Comprobamos:
8x - 15x - 30x - 51x = 53x + 31x - 172
8 . 1 - 15 . 1 - 30 . 1 - 51 . 1 = 53 . 1 + 31 . 1 - 172
8 - 15 - 30 - 51 = 53 + 31 - 172
-88 = -88
k) Solución:
3x + 101 - 4x -33 = 108 - 16x - 100
3x - 4x + 16x = 108 - 100 - 101 + 33
15x = -60
x = -60 : 15
x = -4
Comprobamos:
3x + 101 - 4x - 33 = 108 - 16x - 100
3 . (-4) + 101 - 4 . (-4) - 33 = 108 - 16 . (-4) - 100
-12 + 101 - (-16) - 33 = 108 - (-64) -100
-12 + 101 + 16 - 33 = 108 + 64 - 100
72 = 72
l) Solución:
16 + 7x - 5 + x = 11x - 3 - x
7x + x - 11x + x = -3 - 16 + 5
-2x = -14
x = - 14 : -2
x = 7
Comprobamos:
16 + 7x - 5 + x = 11x - 3 - x
16 + 7 . 7 - 5 + 7 = 11 . 7 - 3 - 7
16 + 49 - 5 + 7 = 77 - 3 - 7
67 = 67