Solve for the variable. show steps for solution pleasee:D?

Question

a)8x - 22 = -60

b)1/2x - 37 = -84

c)3x/4 = 6/7

d)9a + 15 =10a - 7

Answer 1

a) 8x - 22 = -60

8x - 22 + 22 = -60 +22

8x = -38

8x/8 = -38/8

x = -4.75

b) 1/2x - 37 = -84

1/2x - 37 + 37 = -84 +37

1/2x = -47

1/2x * 2  = -47 * 2

x = -94

c) 3x/4 = 6/7

3x/4 * 4/3 = 6/7 * 4/3

x = 24/21

x = 8/7

d) 9a + 15 = 10a - 7

9a - 9a + 15 + 7 = 10a - 9a - 7 +7

22 = (10-9)a

22 = a

Answer 2

a)  8x - 22= -60

=> 8x= -60 + 22

(here now sign of 22 is changed and became +ve bcoz when a  number goes to other side of equal then its sign be changed so here -22 goes to other side of equal and now sign of 22 became +ve)

=> 8x= -38

=> x= -38/8 (Answer or we can make it in short form)

=> x= - 19/4  (Answer :- here we divide numerator and denominator by 2)

b) 1/2x = -84+37

=> 1/2x= -47

=> x= 2* -47

=> x= - 94 ( Answer)

c) 3x/4= 6/7

=> 3x* 7= 6*4

=> 21x= 24

=>x= 24/ 21

=>x= 8/7 (Answer)

d) 9a + 15 = 10a -7

=> 9a - 10a = -7 - 15

=> -a = - 22

=> a = 22 (Answer)

Answer 3

Problem a):

8x - 22 = - 60

4x - 11 = - 30

4x = - 19

x = - 19/4 or - 4 3/4

Answer: x = - 19/4 or - 4 3/4

Proof:

8(- 19/4) - 22 = - 60

- 38 - 22 = - 60

- 60 = - 60

Problem b):

1/2x - 37 = - 84

x - 74 = - 168

x = - 94

Answer: x = - 94

Proof:

1/2(- 94) - 37 = - 84

- 47 - 37 = - 84

- 84 = - 84

Problem c):

3x/4 = 6/7

21x = 24

7x = 8

x = 8/7 or 1 1/7

Answer: x = 8/7 or 1 1/7

Proof:

(3[8/7])/4 = 6/7

(24/7)/4 = 6/7

6/7 = 6/7

Problem d):

9a + 15 = 10a - 7

a = 22

Answer: a = 22

Proof:

9(22) + 15 = 10(22) - 7

198 + 15 = 220 - 7

213 = 213