Which expression is equivalent to 2/3 – 1/4 x + 1/2 – 1/6?

To simplify the expression ( frac{2}{3} – frac{1}{4}x + frac{1}{2} – frac{1}{6} ), we first combine the constant terms:

1. Finding a common denominator for the constants ( frac{2}{3}, frac{1}{2}, ) and ( -frac{1}{6} ). The least common multiple of 3, 2, and 6 is 6.

[

frac{2}{3} = frac{4}{6}, quad frac{1}{2} = frac{3}{6}, quad -frac{1}{6} = -frac{1}{6}

]

2. Combine the constants:

[

frac{4}{6} + frac{3}{6} – frac{1}{6} = frac{4 + 3 – 1}{6} = frac{6}{6} = 1

]

3. The expression now looks like this:

[

1 – frac{1}{4}x

]

4. Now, comparing with the given options, we need to express it as:

[

1 – frac{1}{4}x = frac{12}{12} – frac{3}{