Solve for x:
15+9 (2 x-5) = 15+5 (2 x+7)
9 (2 x-5) = 18 x-45:
18 x-45+15 = 15+5 (2 x+7)
Grouping like terms, 18 x-45+15 = 18 x+(15-45):
18 x+(15-45) = 15+5 (2 x+7)
15-45 = -30:
18 x+-30 = 15+5 (2 x+7)
5 (2 x+7) = 10 x+35:
18 x-30 = 10 x+35+15
Add like terms. 15+35 = 50:
18 x-30 = 10 x+50
Subtract 10 x from both sides:
(18 x-10 x)-30 = (10 x-10 x)+50
18 x-10 x = 8 x:
8 x-30 = (10 x-10 x)+50
10 x-10 x = 0:
8 x-30 = 50
Add 30 to both sides:
8 x+(30-30) = 50+30
30-30 = 0:
8 x = 50+30
50+30 = 80:
8 x = 80
Divide both sides of 8 x = 80 by 8:
(8 x)/8 = 80/8
8/8 = 1:
x = 80/8
The gcd of 80 and 8 is 8, so 80/8 = (8×10)/(8×1) = 8/8×10 = 10:
Answer: |x = 10
