Question

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:
\[
\boxed{\frac{3}{4}}
\]