How to solve these equations?

Question

My teacher didn't give us any notes and im so clueless! =[

1) 5x/4 + 1/2 = x - 1/2

2) x/5 - x/2 = 3

3)3/2(z+5) - 1/4(z+24) = 0

4) 3x/2 + 1/4(x-2) +10

5) 100-4u/3 = 5u+6/4 + 6

Answer 1

1st problem:

5x/4 + 1/2 = x - 1/2

5x/4 = x - 1

5x = 4x - 4

x = - 4

Answer: x  = - 4

Proof:

5(-4)/4 + 1/2 = - 4 - 1/2

- 5 + 1/2 = - 4 - 1/2

- 4 1/2 = - 4 1/2

2nd problem:

x/5 - x/2 = 3

2x - 5x = 30

3x = - 30

x = - 10

Answer: x =  - 10

Proof:

- 10/5 - (- 10/2) = 3

- 2 - (- 5) = 3

- 2 + 5 = 3

3 = 3

3rd problem:

3/2(z + 5) - 1/4(z + 24) = 0

6(z + 5) - (z + 24) = 0

6z + 30 - z - 24 = 0

5z = - 6

z =  - 6/5 or - 1/1/5

Answer: z = - 6/5 or - 1 1/5

Proof:

3/2(- 6/5 + 5) - 1/4(- 6/5 + 24) = 0

3/2(- 6/5 + 25/5) - 1/4(- 6/5 + 120/5) = 0

3/2(19/5) - 1/4(114/5) = 0

57/10 - 114/20 = 0

57/10 - 57/10 = 0

0 = 0

4th problem:

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

= 3/2x + 1/4x - 1/2 + 10

= 6/4x + 1/4x - 1/2 + 20/2

= 5/4x + 19/2

= 1 1/4x + 9 1/2

Answer: 1 1/4x + 9 1/2

5th problem:

(100 - 4u)/3 = (5u + 6)/4 + 6

1/3(100 - 4u) = 1/4(5u + 6) + 6

100/3 - 4/3u = 5/4u + 3/2 + 6

5/4u + 4/3u = 100/3 - 3/2 - 6

15/12u + 16/12u = 200/6 - 9/6 - 36/6

31/12u = 155/6

u = 12/31(155/6)

u = 10

Answer: u = 10

(100 - 4[10])/3 = (5[10] + 6)/4 + 6

(100 - 40)/3 = (50 + 6)/4 + 6

60/3 = 56/4 + 6

20 = 14 + 6

20 = 20

Answer 2

1) 5x/4 + 1/2 = x - 1/2

5x/4-x=1/2-1/2

x(5/4-1)=0

x=0/(5/4-1)=0

2) x/5 - x/2 = 3

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

x=3/(-3/10)

x=-10

3)3/2(z+5) -  1/4(z+24)= 0

3/2(z+5)=1/4(z+24)

(z+5)=[1/4(z+24)]/3/2

z+5=z/6+4

z-z/6=4-5

z=-1/(5/6)

z=-6/5

4) 3x/2 + 1/4(x-2) +10

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

3x/2 +x/4-1/2=-10

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

x=(-19/2)/(7/4)

x=-38/7

5) 100-4u/3 = 5u+6/4 + 6

4u/3-5u  = -100+ 6+6/4

u(4/3-5)=(-96+6/4)

u=(-96+6/4)/(-11/3)