Question

ayuda a pepito a relacionar cada ecuación con su solución

Answer 1

Ayudando a Pepito a relacionar cada ecuación con su solución nos queda:

• 1-. x - (5x - 1)/3 = 4x - 3/5 → x = 1/5
• 2-. 10x - (8x - 3)/4 = 2(x - 3) → x = -9/8
• 3-. (x- 2)/3 - (x - 3)/4 = (x - 4)/5 → x = 53/7
• 4-. (x- 1)/2 - (x - 2)/3 - (x - 3)/4 = -(x - 5)/5 → x = 5/7
• 5-. x - (5x - 1) - (7 - 5x)/10 = 1 → x = -1/5
• 6-. 2x - (5x - 6)/4 + 1/3(x - 5) = -5x → x = 2/73
• 7-. 4 - (10x + 1)/6 = 4x - (16x + 3)/4 → x = 11/4
• 8-. 1/2(x - 1) - (x - 3) = 1/3(x + 3) + 1/6 → x = 8/5
• 9-. (6x + 1)/3 - (11x - 2)/9 - 1/4(5x - 2) = 5/6(6x + 1) →  x = 8/197
• 10- (4x + 1)/3 = 1/3(4x - 1) - (13 + 2x)/6 - 1/2(x - 3) → x = -8/5

¿Qué es una ecuación?

Son dos expresiones matemáticas que se igualan, estas son separadas por el signo de igualdad ("="). En las ecuaciones podemos encontrar datos que pueden ser conocidos o no.

Resolviendo:

• 1-. x - (5x - 1)/3 = 4x - 3/5

x - (5x - 1)/3 = 4x - 3/5

3x - 5x + 1 = 12x - 9/5

15x - 25x + 5 = 60x - 9

60x + 25x - 15x = 9 + 5

70x = 14

x = 14/70

x = 1/5

• 2-. 10x - (8x - 3)/4 = 2(x - 3)

10x - (8x - 3)/4 = 2(x - 3)

40x - 8x + 3 = 8x - 24

40x - 8x - 8x = -24 - 3

24x = -27

x = -27/24

x = -9/8

• 3-. (x- 2)/3 - (x - 3)/4 = (x - 4)/5

(x- 2)/3 - (x - 3)/4 = (x - 4)/5

4*5(x- 2) - 3*5(x - 3) = 3*4(x - 4)

20(x- 2) - 15(x - 3) = 12(x - 4)

20x - 40 - 15x + 45 = 12x - 48

20x - 15x - 12x = - 48 - 45 + 40

-7x = -53

x = 53/7

4-. (x- 1)/2 - (x - 2)/3 - (x - 3)/4 = -(x - 5)/5

(x- 1)/2 - (x - 2)/3 - (x - 3)/4 = -(x - 5)/5

(x- 1) - 2(x - 2)/3 - 2(x - 3)/4 = -2(x - 5)/5

3(x- 1) - 2(x - 2) - 2*3(x - 3)/4 = -2*3(x - 5)/5

3*4(x- 1) - 2*4(x - 2) - 2*3(x - 3) = -2*3*4(x - 5)/5

3*4*5(x- 1) - 2*4*5(x - 2) - 2*3*5(x - 3) = -2*3*4(x - 5)

3*4*5(x- 1) - 2*4*5(x - 2) - 2*3*5(x - 3) = -2*3*4(x - 5)

60(x- 1) - 40(x - 2) - 30(x - 3) = -24(x - 5)

60x - 60 - 40x + 80 - 30x + 90 = -24x + 120

60x - 40x - 30x + 24x = 120 + 60 - 80 - 90

14x = 10

x = 10/14

x = 5/7

5-. x - (5x - 1) - (7 - 5x)/10 = 1

10x - 10(5x - 1) - (7 - 5x) = 10

10x - 50x + 10 - 7 + 5x = 10

10x - 50x + 5x = 10 - 10 + 7

-35x = 7

x = -7/35

x = -1/5

• 6-. 2x - (5x - 6)/4 + 1/3(x - 5) = -5x

2x - (5x - 6)/4 + 1/3(x - 5) = -5x

8x -5x + 6 + 4/3(x - 5) = -20x

24x -15x + 18 + 4(x - 5) = -60x

24x -15x + 18 + 4x - 20 = -60x

24x - 15x + 60x + 4x = 20 - 18

73x = 2

x = 2/73

• 7-. 4 - (10x + 1)/6 = 4x - (16x + 3)/4

4 - (10x + 1)/6 = 4x - (16x + 3)/4

24 - 10x - 1 = 24x - (96x + 18)/4

96 - 40x - 4 = 96x - 96x - 18

-40x = -18 + 4 -96

-40x  = -110

x = 110/40

x = 11/4

• 8-. 1/2(x - 1) - (x - 3) = 1/3(x + 3) + 1/6

1/2(x - 1) - (x - 3) = 1/3(x + 3) + 1/6

x - 1 - 2x + 6 = 1/3(2x + 6) + 1/3

3x - 3 - 6x + 18 = 2x + 6 + 1

3x - 6x - 2x = 6 + 1 - 18 + 3

-5x = -8

x = 8/5

• 9-. (6x + 1)/3 - (11x - 2)/9 - 1/4(5x - 2) = 5/6(6x + 1)

6x + 1 - (11x - 2)/3 - 1/4(15x - 6) = 5/2(6x + 1)

18x + 3 - 11x + 2 - 1/4(45x - 18) = 5/2(18x + 3)

72x + 12 - 44x + 8 -45x + 18 = 180x + 30

72x - 44x - 45x - 180x = 30 - 12 - 8 - 18

72x - 44x - 45x - 180x = 30 - 12 - 8 - 18

-197x = -8

x = 8/197

• 10- (4x + 1)/3 = 1/3(4x - 1) - (13 + 2x)/6 - 1/2(x - 3)

4x + 1 = 4x - 1 - (13 + 2x)/2 - 1/2(3x - 9)

8x + 2 = 8x - 2 - 13 - 2x - 3x + 9

8x - 8x + 2x + 3x = -2 - 13 + 9 - 2

5x = -8

x = -8/5

Si deseas tener más información acerca de ecuaciones, visita:

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