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Question

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

34
Start Fraction 3 over 4 End Fraction

−113
negative Start Fraction 11 over 3 End Fraction

−1112
negative Start Fraction 11 over 12 End Fraction

3

1 answer

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

  1. Start by isolating the term involving \( x \): \[ -2x = \frac{1}{6} - \frac{5}{3} \]

  2. To subtract the fractions, find a common denominator. The least common multiple of 6 and 3 is 6: \[ -2x = \frac{1}{6} - \frac{5 \times 2}{3 \times 2} = \frac{1}{6} - \frac{10}{6} \]

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

  4. Simplify: \[ -2x = \frac{-3}{2} \]

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

Thus, the solution to the equation is \( \frac{3}{4} \).

So, the correct response is Start Fraction 3 over 4 End Fraction.