Solve for x:
x-1/2 = x/4+3
Put each term in x-1/2 over the common denominator 2: x-1/2 = (2 x)/2-1/2:
(2 x)/2-1/2 = x/4+3
(2 x)/2-1/2 = (2 x-1)/2:
(2 x-1)/2 = x/4+3
Put each term in x/4+3 over the common denominator 4: x/4+3 = x/4+12/4:
(2 x-1)/2 = x/4+12/4
x/4+12/4 = (x+12)/4:
(2 x-1)/2 = (x+12)/4
Multiply both sides by 4:
(4 (2 x-1))/2 = (4 (x+12))/4
4/2 = (2×2)/2 = 2:
2 (2 x-1) = (4 (x+12))/4
(4 (x+12))/4 = 4/4×(x+12) = x+12:
2 (2 x-1) = x+12
Expand out terms of the left hand side:
4 x-2 = x+12
Subtract x from both sides:
(4 x-x)-2 = (x-x)+12
4 x-x = 3 x:
3 x-2 = (x-x)+12
x-x = 0:
3 x-2 = 12
Add 2 to both sides:
3 x+(2-2) = 12+2
2-2 = 0:
3 x = 12+2
12+2 = 14:
3 x = 14
Divide both sides of 3 x = 14 by 3:
(3 x)/3 = 14/3
3/3 = 1:
Answer: |x = 14/3
