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$\\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?

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$\\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?

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

Choice B is correct. Subtracting 4 from both sides of $\\sqrt{2x+6}+4=x+3$ isolates the radical expression on the left side of the equation as follows: $\\sqrt{2x+6}=x-1$. Squaring both sides of $\\sqrt{2x+6}=x-1$ yields $2x+6=x^{2}-2x+1$. This equation can be rewritten as a quadratic equation in standard form: $x^{2}-4x-5=0$. One way to solve this quadratic equation is to factor the expression $x^{2}-4x-5$ by identifying two numbers with a sum of $-4$ and a product of $-5$. These numbers are $-5$ and $1$. So the quadratic equation can be factored as $(x-5)(x+1)=0$. It follows that $5$ and $-1$ are the solutions to the quadratic equation. However, the solutions must be verified by checking whether $5$ and $-1$ satisfy the original equation, $\\sqrt{2x+6}+4=x+3$. When $x=-1$, the original equation gives $\\sqrt{2(-1)+6}+4=(-1)+3$, or $6=2$ , which is false. Therefore, $-1$ does not satisfy the original equation. When $x=5$, the original equation gives $\\sqrt{2(5)+6}+4=5+3$, or $8=8$, which is true. Therefore, $x=5$ is the only solution to the original equation, and so the solution set is $\\{5\\}$.

Choices A, C, and D are incorrect because each of these sets contains at least one value that results in a false statement when substituted into the given equation. For instance, in choice D, when 0 is substituted for x into the given equation, the result is $\\sqrt{2(0)+6}+4=0+3$, or $\\sqrt{6}+4=3$. This is not a true statement, so 0 is not a solution to the given equation.

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$\\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?

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

$\\{-1\\}$

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

$\\{-1,5\\}$

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

$\\{0,-1,5\\}$

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

$\\{5\\}$

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

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-66"}

$\\sqrt{2x + 6} + 4 = x + 3$What is the solution set of the equation above?

$\\sqrt{2x + 6} + 4 = x + 3$What is the solution set of the equation above?

$\\sqrt{2x + 6} + 4 = x + 3$What is the solution set of the equation above?

$\\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?

$\\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?

$\\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?

$\sqrt{2x + 6} + 4 = x + 3$What is the solution set of the equation above?

$\sqrt{2x + 6} + 4 = x + 3$

What is the solution set of the equation above?