Which expression is equivalent to 2/3 – 1/4 x + 1/2 – 1/6?
5/12 + 1/3 x
11/12 + 2/3 x
5/6 + 3/4 x
1/2 + 1/4 x
Which expression is equivalent to 2/3 – 1/4 x + 1/2 – 1/6?
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Which expression is equivalent to 2/3 – 1/4 x + 1/2 – 1/6?
5/12 + 1/3 x
11/12 + 2/3 x
5/6 + 3/4 x
1/2 + 1/4 x
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}{