4n-30=2(2n+15) Which of the following best describes the solutions to the equation shown? Choose 1 answer: (A) There is exactly one solution, n=0. (B) There is exactly one solution, n=-(15)/(4). (C) There are no solutions. (D) There are infinitely many solutions.

Expand and Simplify: First, we need to simplify and solve the equation. Let's start by expanding the right side of the equation. 4n - 30 = 2(2n + 15) 4n - 30 = 4n + 30Isolate Constant Terms: Now, we subtract 4n from both sides to isolate the constant terms. 4n - 4n - 30 = 4n - 4n + 30 0 - 30 = 0 + 30Combine Like Terms: Simplify the equation by combining like terms. -30 = 30Identify Contradiction: We see that -30 does not equal 30, which indicates that there is a contradiction. This means there are no solutions to the equation.

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Algebra 2

Conjugate root theorems

Full solution

4n-30=2(2n+15)

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Which of the following best describes the solutions to the equation shown?

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Choose

1

answer:

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(A) There is exactly one solution,

n=0

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(B) There is exactly one solution,

n=-\frac{15}{4}

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(D) There are infinitely many solutions.

Expand and Simplify: First, we need to simplify and solve the equation. Let's start by expanding the right side of the equation. $\newline$ $4n - 30 = 2(2n + 15)$ $\newline$ $4n - 30 = 4n + 30$
Isolate Constant Terms: Now, we subtract $4n$ from both sides to isolate the constant terms. $\newline$ $4n - 4n - 30 = 4n - 4n + 30$ $\newline$ $0 - 30 = 0 + 30$
Combine Like Terms: Simplify the equation by combining like terms. $\newline$ $-30 = 30$
Identify Contradiction: We see that $-30 \neq 30$ , which indicates that there is a contradiction. This means there are no solutions to the equation.