5/3-2x=1/6

Answer 1

To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), follow these steps:

1. Isolate the term with \( x \): \[ -2x = \frac{1}{6} - \frac{5}{3} \]

2. Find a common denominator for the fractions on the right side. The least common multiple of 6 and 3 is 6. Convert \( \frac{5}{3} \) to sixths: \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]

3. Now subtract: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = \frac{-9}{6} \]

4. Simplify: \[ \frac{-9}{6} = \frac{-3}{2} \] So, we have: \[ -2x = -\frac{3}{2} \]

5. Divide both sides by -2: \[ x = \frac{-\frac{3}{2}}{-2} = \frac{3}{4} \]

Thus, the solution is: \[ \boxed{\frac{3}{4}} \]