Question

Resuelve las siguientes ecuaciones lineales: a) (4x-3)/2= (5x+1)/3 b) (x-3)/2 +7= x- (5-x)/4 c) (-3(5-x))/10 - 3x/2 = 7- 5x/3 d) (3(x+1))/2 –x = (x-4)/3 e) (x+2)/2 – 3 (x+1) = 5x/2 -2

Answer 1

Respuesta:

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

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

12x-9 = 10x+2

(12-10)x = 2+9

2x = 11

2x/2 = 11/2

x = 11/2

b) (x-3)/2 +7 = x- (5-x)/4 ; m.c.m(2,4,7) = 28

28((x-3)/2)+28(7) = 28(x)-28((5-x)/4)

14(x-3)+196 = 28x-7(5-x)

14x-42+196 = 28x-36+7x

14x+154 = (28+7)x-36

14x+154 = 35x-36

154+36 = 35x-14x

190 = 21x

21x = 190

21x/21 = 190/21

x = 190/21

c) (-3(5-x))/10 - (3x)/2 = 7- (5x)/3 ; m.c.m(2,3,10) = 30

30(-3(5-x))/10)-30((3x)/2) = 30(7)-30((5x)/3)

3(-3(-5-x))-15(3x) = 210-10(5x)

3(15+3x)-45x = 210-50x

45+9x-45x = 210-50x

45+(-36x) = 210-50x

45-36x = 210-50x

-36x+50x = 210-45

14x = 165

14x/14 = 165/14

x = 165/14

d) (3(x+1))/2 –x = (x-4)/3 ; m.c.m(2,3) = 6

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

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

3(3x+3)-6x = 2x-8

9x+9-6x = 2x-8

3x+9 = 2x-8

(3-2)x = -8-9

x = -17

e) (x+2)/2 – 3 (x+1) = 5x/2 -2

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

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

x+2-6x-6 = 5x-4

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

-5x+(-4) = 5x-4

-5x-4 = 5x-4

(-5-5)x = -4+4

-10x = 0

-10x/-1 = 0/-1

10x = 0

10x/10 = 0/10

x = 0

Explicación paso a paso: