Solve for x:
(4 x)/(5) - 3 = 7 - (x)/(2)
Put each term in (4 x)/(5) - 3 over the common denominator 5: (4 x)/(5) - 3 = (4 x)/5 - (15)/5:
(4 x)/5 - (15)/5 = 7 - (x)/(2)
(4 x)/5 - (15)/5 = (4 x - 15)/5:
1/5 (4 x - 15) = 7 - (x)/(2)
Put each term in 7 - (x)/(2) over the common denominator 2: 7 - (x)/(2) = 14/2 - (x)/2:
(4 x - 15)/5 = 14/2 - x/2
14/2 - x/2 = (14 - x)/2:
(4 x - 15)/5 = (14 - x)/2
Multiply both sides by 10:
(10 (4 x - 15))/5 = (10 (14 - x))/2
10/5 = (5×2)/5 = 2:
2 (4 x - 15) = (10 (14 - x))/2
10/2 = (2×5)/2 = 5:
2 (4 x - 15) = 5 (14 - x)
Expand out terms of the left hand side:
8 x - 30 = 5 (14 - x)
Expand out terms of the right hand side:
8 x - 30 = 70 - 5 x
Add 5 x to both sides:
8 x + 5 x - 30 = (5 x - 5 x) + 70
5 x - 5 x = 0:
8 x + 5 x - 30 = 70
8 x + 5 x = 13 x:
13 x - 30 = 70
Add 30 to both sides:
13 x + (30 - 30) = 70 + 30
30 - 30 = 0:
13 x = 70 + 30
70 + 30 = 100:
13 x = 100
Divide both sides of 13 x = 100 by 13:
(13 x)/13 = 100/13
13/13 = 1:
Answer: |x = 100/13=7 9/13
