Solve the equation

(x/8)-(x/2)=6+(6x/16)

\(\frac{x}{8}-\frac{x}{2}=6+\frac{6x}{16} \)    [least common multiple = 16

\(\frac{2x-8x}{16} =\frac{16* 6+6}{16} \)       [ add, subtr, multiply 16 

\(-6x=102\)               [ / - 6

\(x=-17\)     !

Solve for x:
(-3 x)/(8) = (3 x)/8 + 6

Put each term in (3 x)/8 + 6 over the common denominator 8: (3 x)/8 + 6 = (3 x)/8 + 48/8:
(-3 x)/(8) = (3 x)/8 + 48/8

(3 x)/8 + 48/8 = (3 x + 48)/8:
(-3 x)/(8) = (3 x + 48)/8

Multiply both sides by 8:
(-3×8 x)/(8) = (8 (3 x + 48))/8

(8 (-3) x)/8 = 8/8×-3 x = -3 x:
-3 x = (8 (3 x + 48))/8

(8 (3 x + 48))/8 = 8/8×(3 x + 48) = 3 x + 48:
-3 x = 3 x + 48

Subtract 3 x from both sides:
-3 x - 3 x = (3 x - 3 x) + 48

-3 x - 3 x = -6 x:
-6 x = (3 x - 3 x) + 48

3 x - 3 x = 0:
-6 x = 48

Divide both sides of -6 x = 48 by -6:
(-6 x)/(-6) = 48/(-6)

(-6)/(-6) = 1:
x = 48/(-6)

The gcd of 48 and -6 is 6, so 48/(-6) = (6×8)/(6 (-1)) = 6/6×8/(-1) = 8/(-1):
x = 8/(-1)

Multiply numerator and denominator of 8/(-1) by -1:
Answer: |x = -8