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$3(2x-6)-11=4(x-3)+6$

If $x$ is the solution to the equation above, what is the value of $x-3$?

","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-31"}],"about":{"@type":"Thing","name":"Math, Algebra, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Algebra","Duplicate"],"name":"

$3(2x-6)-11=4(x-3)+6$

If $x$ is the solution to the equation above, what is the value of $x-3$?

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

Choice B is correct. Because 2 is a factor of both $2x$ and 6, the expression $2x-6$ can be rewritten as $2(x-3)$. Substituting $2(x-3)$ for $2x-6$ on the left-hand side of the given equation yields $3(2)(x-3)-11=4(x-3)+6$, or $6(x-3)-11=4(x-3)+6$ Subtracting $4(x-3)$ from both sides of this equation yields $2(x-3)-11=6$ Adding $11$ to both sides of this equation yields $2(x-3)=17$ Dividing both sides of this equation by $2$ yields $x-3=\\dfrac{17}{2}$.

Alternate approach: Distributing $3$ to the quantity $2x-6$ on the left-hand side of the given equation and distributing $4$ to the quantity $x-3$ on the right-hand side yields $6x-18-11=4x-12+6$, or $6x-29=4x-6$ Subtracting $4x$ from both sides of this equation yields $2x-29=-6$ Adding $29$ to both sides of this equation yields $2x=23$ Dividing both sides of this equation by $2$ yields $x=\\dfrac{23}{2}$ Therefore, the value of $x-3$ is $\\dfrac{23}{2}-3$, or $\\dfrac{17}{2}$.

Choice A is incorrect. This is the value of $x$, not $x-3$. Choices C and D are incorrect. If the value of $x-3$ is $\\dfrac{15}{2}$ or $-\\dfrac{15}{2}$, it follows that the value of x is $\\dfrac{21}{2}$ or $-\\dfrac{9}{2}$, respectively. However, solving the given equation for x yields $x=\\dfrac{23}{2}$. Therefore, the value of $x-3$ can't be $\\dfrac{15}{2}$ or $-\\dfrac{15}{2}$.

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

$3(2x-6)-11=4(x-3)+6$

If $x$ is the solution to the equation above, what is the value of $x-3$?

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

$\\frac{23}{2}$

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

$\\frac{15}{2}$

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

$-\\frac{15}{2}$

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

$\\frac{17}{2}$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-algebra-multiple-choice-question-31"}

$3(2x-6)-11=4(x-3)+6$If $x$ is the solution to the equation above, what is the value of $x-3$?

$3(2x-6)-11=4(x-3)+6$If $x$ is the solution to the equation above, what is the value of $x-3$?

$3(2x-6)-11=4(x-3)+6$If $x$ is the solution to the equation above, what is the value of $x-3$?

$3(2x-6)-11=4(x-3)+6$

If $x$ is the solution to the equation above, what is the value of $x-3$?

$3(2x-6)-11=4(x-3)+6$

If $x$ is the solution to the equation above, what is the value of $x-3$?

$3(2x-6)-11=4(x-3)+6$

If $x$ is the solution to the equation above, what is the value of $x-3$?