Question

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

3
3

−1112
negative Start Fraction 11 over 12 End Fraction

−113
negative Start Fraction 11 over 3 End Fraction

34

1 answer

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

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

  2. To subtract the fractions, we need a common denominator. The common denominator of 6 and 3 is 6. Rewrite \( \frac{5}{3} \) with a denominator of 6: \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]

  3. Now we can perform the subtraction: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = \frac{-9}{6} \] Simplifying \( \frac{-9}{6} \) gives: \[ -2x = \frac{-3}{2} \]

  4. Now, 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: \[ x = \frac{3}{4} \]

From the responses you provided, the correct answer is: \( \frac{3}{4} \).