Check my multi-step equations answers?

Question

1.
-57=3(1-5x)
x=8
2.
45=6+3(1-4x)
x=12
3.
-1=-2(a+1)-3
x= -3
4.
1= -k (-)(-2k-2)
k=3

5
-51=-3(-1+3p)
p=15
6.
-6x-6(-1-4x)=42
x= ??? What is it?
7. 4(n+5)=24
n=1
8.
-24=-6(m+1)
m= 3
9.
-(r-6)= 11
r=17
10.
6(5x+5)= -30

Answer 1

Distributive property: a(b+c)=ab+ac
1.
-57=3(1-5x)
-57=3-15x
-60=-15x
x=4

2.
45=6+3(1-4x)
45=6+3-12x
45=9-12x
36=-12x
x=-3

3.
-1=-2(a+1)-3
-1=-2a-2-3
-1=-2a-5
-1+5=-2a
4=-2a
a=-2

5
-51=-3(-1+3p)
-51=3-9p
-54=-9p
p=6

6.
-6x-6(-1-4x)=42
-6x+6+24x=42
18x=26
x=2


7.
4(n+5)=24
4n+20=24
4n=4
n=1

8.
-24=-6(m+1)
-24=-6m-6
-18=-6m
m= 3
9.
-(r-6)= 11
-r+6=11
-r=11-6=5
r=-5
10.
6(5x+5)=-30
30x+30=-30
30x=-60
x=-2

Comments

4).

1 = - k (-)(- 2k - 2)

1 = - k + 2k + 2

1 = k + 2

k = 1 - 2

⇒ k = - 1.

6).

- 6x - 6(- 1 - 4x) = 42.

- 6x + 6 + 24x = 42

18x = 42 - 6

18x = 36

x = 36/18

⇒ x = 2.