Question

What is the solution of the equation 5/3−2x=1/6 ?(1 point)
Responses

−113
negative Start Fraction 11 over 3 End Fraction

3
3

−1112
negative Start Fraction 11 over 12 End Fraction

34
Start Fraction 3 over 4 End Fraction

Answer 1

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

1. **Isolate the term involving \( x \)**:

\[
-2x = \frac{1}{6} - \frac{5}{3}
\]

2. **To perform the subtraction, convert \( \frac{5}{3} \) to have a common denominator with \( \frac{1}{6} \)**. The common denominator is 6.

\[
\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}
\]

So now we can rewrite the equation:

\[
-2x = \frac{1}{6} - \frac{10}{6}
\]
\[
-2x = \frac{1 - 10}{6} = \frac{-9}{6}
\]
\[
-2x = \frac{-3}{2} \quad \text{(by simplifying } \frac{-9}{6}\text{)}
\]

3. **Now, divide both sides by -2 to solve for \( x \)**:

\[
x = \frac{-3/2}{-2} = \frac{-3}{2} \times \frac{1}{-2} = \frac{3}{4}
\]

Thus, the solution to the equation \( \frac{5}{3} - 2x = \frac{1}{6} \) is:

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

Therefore, the correct response is:

**34 (Start Fraction 3 over 4 End Fraction)**.