To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), follow these steps:
- First, isolate the term with \( x \) by subtracting \( \frac{5}{3} \) from both sides:
\[ -2x = \frac{1}{6} - \frac{5}{3} \]
- To subtract the fractions, you need a common denominator. The common denominator between 6 and 3 is 6. Rewrite \( \frac{5}{3} \) with a denominator of 6:
\[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]
Now substitute that back into the equation:
\[ -2x = \frac{1}{6} - \frac{10}{6} \]
- Perform the subtraction:
\[ -2x = \frac{1 - 10}{6} = \frac{-9}{6} \]
- Simplify the fraction:
\[ -2x = \frac{-3}{2} \]
- Now, to solve for \( x \), divide both sides by -2:
\[ x = \frac{-3/2}{-2} = \frac{-3}{2} \times \frac{1}{-2} = \frac{3}{4} \]
Thus, the solution to the equation is:
\[ \boxed{\frac{3}{4}} \]