5/3x-1/6=x-1/4

Step 1: Eliminate the fractions by finding a common denominator. The common denominator for 3, 6, and 4 is 12.
12 \left(\frac{5}{3}x - \frac{1}{6}\right) = 12 \left(x - \frac{1}{4}\right)

Step 2: Distribute 12 to each term inside the parentheses.
12 \cdot \frac{5}{3}x - 12 \cdot \frac{1}{6} = 12 \cdot x - 12 \cdot \frac{1}{4}
4 \cdot 5x - 2 = 12x - 3

Step 3: Simplify the equation.
20x - 2 = 12x - 3

Step 4: Move the terms involving x to one side and constant terms to the other side.
20x - 12x = -3 + 2
8x = -1

Step 5: Solve for x.
x = \frac{-1}{8}