What is the solution of the equation 5/3−2x=1/6

Question

?(1 point)
Responses

−11/3
negative Start Fraction 11 over 3 End Fraction

3/4
Start Fraction 3 over 4 End Fraction

−11/12
negative Start Fraction 11 over 12 End Fraction

3

Answer 1

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

1. Subtract \( \frac{5}{3} \) from both sides: \[ -2x = \frac{1}{6} - \frac{5}{3} \]

2. To combine the right-hand side, we need a common denominator. The common denominator for 6 and 3 is 6. Convert \( \frac{5}{3} \) to sixths: \[ \frac{5}{3} = \frac{10}{6} \]

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

4. Simplify \( \frac{-9}{6} \) to \( \frac{-3}{2} \): \[ -2x = -\frac{3}{2} \]

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

Thus, the solution to the equation \( \frac{5}{3} - 2x = \frac{1}{6} \) is \( \frac{3}{4} \).

The correct response is: \[ \frac{3}{4} \]