Solve for x:
(2 x)/3+4 = (3 x)/(5)-2
Put each term in (2 x)/3+4 over the common denominator 3: (2 x)/3+4 = (2 x)/3+12/3:
(2 x)/3+12/3 = (3 x)/(5)-2
(2 x)/3+12/3 = (2 x+12)/3:
(2 x+12)/3 = (3 x)/(5)-2
Put each term in (3 x)/(5)-2 over the common denominator 5: (3 x)/(5)-2 = (3 x)/5-(10)/5:
(2 x+12)/3 = (3 x)/5-(10)/5
(3 x)/5-(10)/5 = (3 x-10)/5:
(2 x+12)/3 = (3 x-10)/5
Multiply both sides by 15:
(15 (2 x+12))/3 = (15 (3 x-10))/5
15/3 = (3×5)/3 = 5:
5 (2 x+12) = (15 (3 x-10))/5
15/5 = (5×3)/5 = 3:
5 (2 x+12) = 3 (3 x-10)
Expand out terms of the left hand side:
10 x+60 = 3 (3 x-10)
Expand out terms of the right hand side:
10 x+60 = 9 x-30
Subtract 9 x from both sides:
(10 x-9 x)+60 = (9 x-9 x)-30
10 x-9 x = x:
x+60 = (9 x-9 x)-30
9 x-9 x = 0:
x+60 = -30
Subtract 60 from both sides:
x+(60-60) = -30-60
60-60 = 0:
x = -30-60
-30-60 = -90:
Answer: |x = -90
