Solve the following equations. show all work for full credit. part a: 6r − 1 + 6r = 11 (3 points) part b: 8 = 8v − 4(v + 8) (5 points) part c: the quantity of x plus 4 over 3 = 2 (2 points)

A: Solve for r:
6 r + 6 r - 1 = 11

Grouping like terms, 6 r + 6 r - 1 = (6 r + 6 r) - 1:
(6 r + 6 r) - 1 = 11
6 r + 6 r = 12 r:
12 r - 1 = 11

Add 1 to both sides:
12 r + (1 - 1) = 1 + 11

1 - 1 = 0:
12 r = 11 + 1

11 + 1 = 12:
12 r = 12

Divide both sides of 12 r = 12 by 12:
(12 r)/12 = 12/12

12/12 = 1:
r = 12/12
12/12 = 1:
  r = 1


B: 
Solve for v:
8 = 8 v - 4 (v + 8)

-4 (v + 8) = -4 v - 32:
8 = 8 v + -4 v - 32

Grouping like terms, 8 v - 4 v - 32 = (8 v - 4 v) - 32:
8 = (8 v - 4 v) - 32

8 v - 4 v = 4 v:
8 = 4 v - 32

8 = 4 v - 32 is equivalent to 4 v - 32 = 8:
4 v - 32 = 8

Add 32 to both sides:
4 v + (32 - 32) = 32 + 8

32 - 32 = 0:
4 v = 8 + 32

8 + 32 = 40:
4 v = 40

Divide both sides of 4 v = 40 by 4:
(4 v)/4 = 40/4

4/4 = 1:
v = 40/4

The gcd of 40 and 4 is 4, so 40/4 = (4×10)/(4×1) = 4/4×10 = 10:
v = 10


C:  x+4/3=2
x=(2-4)/3
x=(6/3)-4/3
x=(6-4)/3
x=2/3

Patrick earns the most money per hour