Solve for x:
2 (4 + 2 (3 - 5 x)) = 5 (2 + 2 (3 - 3 x))
2 (3 - 5 x) = 6 - 10 x:
2 (6 - 10 x + 4) = 5 (2 + 2 (3 - 3 x))
Add like terms. 4 + 6 = 10:
2 (10 - 10 x) = 5 (2 + 2 (3 - 3 x))
2 (3 - 3 x) = 6 - 6 x:
2 (10 - 10 x) = 5 (6 - 6 x + 2)
Add like terms. 2 + 6 = 8:
2 (10 - 10 x) = 5 (8 - 6 x)
Expand out terms of the left hand side:
20 - 20 x = 5 (8 - 6 x)
Expand out terms of the right hand side:
20 - 20 x = 40 - 30 x
Add 30 x to both sides:
30 x - 20 x + 20 = (30 x - 30 x) + 40
30 x - 30 x = 0:
30 x - 20 x + 20 = 40
30 x - 20 x = 10 x:
10 x + 20 = 40
Subtract 20 from both sides:
10 x + (20 - 20) = 40 - 20
20 - 20 = 0:
10 x = 40 - 20
40 - 20 = 20:
10 x = 20
Divide both sides of 10 x = 20 by 10:
(10 x)/10 = 20/10
10/10 = 1:
x = 20/10
The gcd of 20 and 10 is 10, so 20/10 = (10×2)/(10×1) = 10/10×2 = 2:
Answer: |x = 2
