Answer:
g = 5
Step-by-step explanation:
Solve for g:
4 (g - 1) + 2 (g + 5) = 36
4 (g - 1) = 4 g - 4:
4 g - 4 + 2 (g + 5) = 36
2 (g + 5) = 2 g + 10:
2 g + 10 + 4 g - 4 = 36
Grouping like terms, 4 g + 2 g - 4 + 10 = (4 g + 2 g) + (-4 + 10):
(4 g + 2 g) + (-4 + 10) = 36
4 g + 2 g = 6 g:
6 g + (-4 + 10) = 36
10 - 4 = 6:
6 g + 6 = 36
Subtract 6 from both sides:
6 g + (6 - 6) = 36 - 6
6 - 6 = 0:
6 g = 36 - 6
36 - 6 = 30:
6 g = 30
Divide both sides of 6 g = 30 by 6:
(6 g)/6 = 30/6
6/6 = 1:
g = 30/6
The gcd of 30 and 6 is 6, so 30/6 = (6×5)/(6×1) = 6/6×5 = 5:
Answer: g = 5
