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

$$x-29=(x-a)(x-29)$$

Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?

I. $a$

II. $a+1$

III. 29

","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-128"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

$$x-29=(x-a)(x-29)$$

Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?

I. $a$

II. $a+1$

III. 29

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

Choice C is correct. Subtracting the expression $(x-29)$ from both sides of the given equation yields $0=(x-a)(x-29)-(x-29)$, which can be rewritten as $0=(x-a)(x-29)+(-1)(x-29)$. Since the two terms on the right-hand side of this equation have a common factor of $(x-29)$, it can be rewritten as $0=(x-29)(x-a+(-1))$, or $0=(x-29)(x-a-1)$. Since $x-a-1$ is equivalent to $x-(a+1)$, the equation $0=(x-29)(x-a-1)$ can be rewritten as $0=(x-29)(x-(a+1))$. By the zero product property, it follows that $x-29=0$ or $x-(a+1)=0$. Adding $29$ to both sides of the equation $x-29=0$ yields $x=29$. Adding $a+1$ to both sides of the equation $x-(a+1)=0$ yields $x=a+1$. Therefore, the two solutions to the given equation are $29$ and $a+1$. Thus, only $a+1$ and $29$, not $a$, are solutions to the given equation.

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

Choice B 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":"

$$x-29=(x-a)(x-29)$$

Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?

I. $a$

II. $a+1$

III. 29

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

I and II only

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

I and III only

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

I, II, and III

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

II and III only

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

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

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

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

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

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

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-128"}

$$x-29=(x-a)(x-29)$$Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?I. $a$II. $a+1$III. 29

$$x-29=(x-a)(x-29)$$Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?I. $a$II. $a+1$III. 29

$$x-29=(x-a)(x-29)$$Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?I. $a$II. $a+1$III. 29

$$x-29=(x-a)(x-29)$$

Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?

I. $a$

II. $a+1$

III. 29

$$x-29=(x-a)(x-29)$$

Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?

I. $a$

II. $a+1$

III. 29

$$x-29=(x-a)(x-29)$$

Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?

I. $a$

II. $a+1$

III. 29