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$$-3x+21px=84$$

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

","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-algebra-multiple-choice-question-141"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$$-3x+21px=84$$

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

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

Choice B is correct. A linear equation in one variable has no solution if and only if the equation is false; that is, when there is no value of $x$ that produces a true statement. It's given that in the equation $-3x+21px=84,p$ is a constant and the equation has no solution for $x$. Therefore, the value of the constant $p$ is one that results in a false equation. Factoring out the common factor of $-3x$ on the left-hand side of the given equation yields $-3x(1-7p)=84$. Dividing both sides of this equation by $-3$ yields $x(1-7p)=-28$. Dividing both sides of this equation by $(1-7p)$ yields $x=\\frac{-28}{1-7p}$. This equation is false if and only if $1-7p=0$. Adding $7p$ to both sides of $1-7p=0$ yields $1=7p$. Dividing both sides of this equation by $7$ yields $\\frac{1}{7}=p$. It follows that the equation $x=\\frac{-28}{1-7p}$ is false if and only if $p=\\frac{1}{7}$. Therefore, the given equation has no solution if and only if the value of $p$ is $\\frac{1}{7}$.

Choice A 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.

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$$-3x+21px=84$$

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

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

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

$\\frac{4}{3}$

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

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

$\\frac{1}{7}$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-141"}

$$-3x+21px=84$$In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

$$-3x+21px=84$$In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

$$-3x+21px=84$$In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

$$-3x+21px=84$$

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

$$-3x+21px=84$$

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

$$-3x+21px=84$$

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?