{"@context":"https://schema.org/","@type":"Quiz","name":"

$$f(x)=|59-2x|$$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-60"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$$f(x)=|59-2x|$$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

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

Choice A is correct. The value of $k$ for which $f(k)=3k$ can be found by substituting $k$ for $x$ and $3k$ for $f(x)$ in the given equation, $f(x)=|59-2x|$, which yields $3k=|59-2k|$. For this equation to be true, either $-3k=59-2k$ or $3k=59-2k$. Adding $2k$ to both sides of the equation $-3k=59-2k$ yields $-k=59$. Dividing both sides of this equation by $-1$ yields $k=-59$. To check whether $-59$ is the value of $k$, substituting $-59$ for $k$ in the equation $3k=|59-2k|$ yields $3(-59)=|59-2(-59)|$, which is equivalent to $-177=|177|$, or $-177=177$, which isn't a true statement. Therefore, $-59$ isn't the value of $k$. Adding $2k$ to both sides of the equation $3k=59-2k$ yields $5k=59$. Dividing both sides of this equation by $5$ yields $k=\\frac{59}{5}$. To check whether $\\frac{59}{5}$ is the value of $k$, substituting $\\frac{59}{5}$ for $k$ in the equation $3k=|59-2k|$ yields $3\\big(\\frac{59}{5})=|59-2(\\frac{59}{5})|$, which is equivalent to $\\frac{177}{5}=|\\frac{177}{5}|$, or $\\frac{177}{5}=\\frac{177}{5}$, which is a true statement. Therefore, the value of $k$ for which $f(k)=3k$ is $\\frac{59}{5}$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

"},"encodingFormat":"text/markdown","text":"

$$f(x)=|59-2x|$$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

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

$\\frac{59}{2}$

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

$\\frac{177}{5}$

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

$59$

"}],"acceptedAnswer":{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$\\frac{59}{5}$

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

Choice D is incorrect and may result from conceptual or calculation errors.

"},"answerExplanation":{"@type":"Comment","text":"

Choice D is incorrect and may result from conceptual or calculation errors.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-60"}

$$f(x)=|59-2x|$$The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

$$f(x)=|59-2x|$$The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

$$f(x)=|59-2x|$$The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

$$f(x)=|59-2x|$$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

$$f(x)=|59-2x|$$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?

$$f(x)=|59-2x|$$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?