Question

Determinem a solução das equações com fração: Para você ganhar mais pontos, por favor coloque como fazer passo a passo cada equação.

Answer 1

Explicação passo-a-passo:

a)

$\sf -\dfrac{4m}{3}-\dfrac{1}{5}=\dfrac{3m}{2}-\dfrac{1}{4}$

$\sf mmc(3,5,4)=60$

$\sf 20\cdot(-4m)-12\cdot1=30\cdot3m-15\cdot1$

$\sf -80m-12=90m-15$

$\sf 90m-15=-80m-12$

$\sf 90m+80m=-12+15$

$\sf 170m=3$

$\sf \red{m=\dfrac{3}{170}}$

b)

$\sf \dfrac{m+5}{3}-\dfrac{5}{2}=-\dfrac{m-6}{3}-\dfrac{2}{3}$

$\sf mmc(3,2)=6$

$\sf 2\cdot(m+5)-3\cdot5=2\cdot(-m+6)-2\cdot2$

$\sf 2m+10-15=-2m+12-4$

$\sf 2m-5=-2m+8$

$\sf 2m+2m=8+5$

$\sf 4m=13$

$\sf \red{m=\dfrac{13}{4}}$

c)

$\sf -\dfrac{6\cdot(m-2)}{5}-\dfrac{2}{3}=\dfrac{1}{2}+\dfrac{5\cdot(m+5)}{3}$

$\sf \dfrac{-6m+12}{5}-\dfrac{2}{3}=\dfrac{1}{2}+\dfrac{5m+25}{3}$

$\sf mmc(5,3,2)=30$

$\sf 6\cdot(-6m+12)-10\cdot2=15\cdot1+10\cdot(5m+25)$

$\sf -36m+72-20=15+50m+250$

$\sf -36m+52=50m+265$

$\sf 50m+265=-36m+52$

$\sf 50m+36m=52-265$

$\sf 86m=-213$

$\sf \red{m=-\dfrac{213}{86}}$

d)

$\sf \dfrac{5\cdot(m-2)}{2}-\dfrac{2\cdot(m+4)}{3}=\dfrac{3\cdot(m-1)}{2}$

$\sf \dfrac{5m-10}{2}-\dfrac{2m+8}{3}=\dfrac{3m-3}{2}$

$\sf mmc(2,3)=6$

$\sf 3\cdot(5m-10)-2\cdot(2m+8)=3\cdot(3m-3)$

$\sf 15m-30-4m-16=9m-9$

$\sf 11m-46=9m-9$

$\sf 11m-9m=-9+46$

$\sf 2m=37$

$\sf \red{m=\dfrac{37}{2}}$

e)

$\sf -\dfrac{(2m+1)}{3}=\dfrac{3\cdot(m-2)}{2}$

$\sf \dfrac{-2m-1}{3}=\dfrac{3m-6}{2}$

$\sf 3\cdot(3m-6)=2\cdot(-2m-1)$

$\sf 9m-18=-4m-2$

$\sf 9m+4m=-2+18$

$\sf 13m=16$

$\sf \red{m=\dfrac{16}{13}}$

f)

$\sf \dfrac{2\cdot(m+4)}{3}=-\dfrac{2\cdot(m-7)}{5}$

$\sf \dfrac{2m+8}{3}=\dfrac{-2m+14}{5}$

$\sf 5\cdot(2m+8)=3\cdot(-2m+14)$

$\sf 10m+40=-6m+42$

$\sf 10m+6m=42-40$

$\sf 16m=2$

$\sf m=\dfrac{2}{16}$

$\sf \red{m=\dfrac{1}{8}}$

Answer 2

Oie, Td Bom?!

a)

- 4m/3 - 1/5 = 3m/2 - 1/4

60(- 4m/3 - 1/5) = 60(3m/2 - 1/4)

- 60 . 4m/3 - 60 . 1/5 = 60 . 3m/2 - 60 . 1/4

- 80m - 12 = 90m - 15

- 80m - 90m = - 15 + 12

- 170m = - 3

m = -3/-170

m = 3/170

b)

[m + 5]/3 - 5/2 = - [m - 6]/3 - 2/3

6([m + 5]/3 - 5/2) = 6(- [m - 6]/3 - 2/3)

6 . [m + 5]/3 - 6 . 5/2 = - 6 . [m - 6]/3 - 6 . 2/3

2(m + 5) - 15 = - 2(m - 6) - 4

2m + 10 - 15 = - 2m + 12 - 4

2m - 5 = - 2m + 8

2m + 2m = 8 + 5

4m = 13

m = 13/4

c)

- [6(m - 2)]/5 - 2/3 = 1/2 + [5(m + 5)]/3

- [6m - 12]/5 - 2/3 = 1/2 + [5m + 25]/3

30(- [6m - 12]/5 - 2/3) = 30(1/2 + [5m + 25]/3)

- 30 . [6m - 12]/5 - 30 . 2/3 = 30 . 1/2 + 30 . [5m + 25]/3

- 6(6m - 12) - 20 = 15 + 10(5m + 25)

- 36m + 72 - 20 = 15 + 50m + 250

- 36m + 52 = 265 + 50m

- 36m - 50m = 265 - 52

- 86m = 213

m = 213/-86

m = - 213/86

d)

[5(m - 2)]/2 - [2(m + 4)]/3 = [3(m - 1)]/2

[5m - 10]/2 - [2m + 8]/3 = [3m - 3]/2

6([5m - 10]/2 - [2m + 8]/3) = 6 . [3m - 3]/2

6 . [5m - 10]/2 - 6 . [2m + 8]/3 = 3(3m - 3)

3(5m - 10) - 2(2m + 8) = 3(3m - 3)

15m - 30 - 4m - 16 = 9m - 9

11m - 46 = 9m - 9

11m - 9m = - 9 + 46

2m = 37

m = 37/2

e)

- [(2m + 1)]/3 = [3(m - 2)]/2

- [2m + 1]/3 = [3m - 6]/2

- [2(2m + 1)]/3 = 3m - 6

- 2(2m + 1) = 3(3m - 6)

- 4m - 2 = 9m - 18

- 4m - 9m = - 18 + 2

- 13m = - 16

m = -16/-13

m = 16/13

f)

[2(m + 4)]/3 = - [2(m - 7)]/5

[2m + 8]/3 = - [2m - 14]/5

[5(2m + 8)]/3 = - (2m - 14)

5(2m + 8) = - 3(2m - 14)

10m + 40 = - 6m + 42

10m + 6m = 42 - 40

16m = 2

m = 2/16

m = [2 ÷ 2]/[16 ÷ 2]

m = 1/8

Att. Makaveli1996