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If $\\frac{1}{2}x-\\frac{1}{6}x=1$, what is the value of $x$?

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If $\\frac{1}{2}x-\\frac{1}{6}x=1$, what is the value of $x$?

","comment":{"@type":"Comment","text":"

Choice C is correct. To make it easier to add like terms on the left-hand side of the given equation, both sides of the equation can be multiplied by 6, which is the lowest common denominator of $\\frac{\\mathbf{1}}{2}$ and $\\frac{\\mathbf{1}}{6}$. This yields $3x-x=6$, which can be rewritten as $2x=6$. Dividing both sides of this equation by 2 yields $x=3$.

Choice A is incorrect and may result from subtracting the denominators instead of numerators with common denominators to get $\\frac{-\\mathbf{1}}{4}x$, rather than $\\frac{1}{3}x$, on the left-hand side of the equation. Choice B is incorrect and may result from rewriting the given equation as $\\frac{1}{2}x=\\frac{1}{6}$ instead of $2x=6$. Choice D is incorrect and may result from conceptual or computational errors.

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If $\\frac{1}{2}x-\\frac{1}{6}x=1$, what is the value of $x$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$-4$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$\\frac{1}{3}$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$6$

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$3$

","comment":{"@type":"Comment","text":"

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"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-167"}

If $\frac{1}{2}x-\frac{1}{6}x=1$, what is the value of $x$?