1/4 (x+6) + 1/8 (x-3) = 1/3 (x+4)

Distribute 1/4 through the parenthesis:

1/4x + 3/2 + 1/8 (x-3) = 1/3 (x+4)

Distribute 1/8 through the parenthesis:

1/4x + 3/2 + 1/8x - 3/8 = 1/3 (x+4)

Distribute 1/3 through the parenthesis:

1/4x + 3/2 + 1/8x - 3/8 = 1/3x + 4/3

Subtract the fractions.

1/4x + 9/8 + 1/8x = 1/3x + 4/3

Multiply both sides of the equation by 24.

6x + 27 + 3x = 8x + 32

Collect the like terms:

9x + 27 = 8x + 32

Move 8 to the left side, then change the sign.

9x - 8x + 27 = 32

Move 27 to the right side, the. change the sign.

9x - 8x = 32 - 27

Collect the like terms.

x = 32 - 27

Subtract the numbers.

32 - 27 = 5

Solution: x = 5