$3(2 n-2)-1=\frac{9}{4}$ $\newline$ Given the equation, what is the value of $2 n-2$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{5}{12}$ $\newline$ (B) $\frac{13}{12}$ $\newline$ (C) $\frac{7}{4}$ $\newline$ (D) $\frac{13}{4}$

Full solution

3(2 n-2)-1=\frac{9}{4}

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Given the equation, what is the value of

2 n-2

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Choose

1

answer:

\newline

(A)

\frac{5}{12}

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(B)

\frac{13}{12}

\newline

(C)

\frac{7}{4}

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(D)

\frac{13}{4}

Simplify Left Side: First, we need to simplify the left side of the equation by distributing the $3$ into the parentheses. $3(2n-2)-1 = 3\times 2n - 3\times 2 - 1$ $= 6n - 6 - 1$ $= 6n - 7$
Set Equal and Solve: Now, we set the simplified expression equal to the right side of the equation and solve for $n$ . $6n - 7 = \frac{9}{4}$
Isolate n: Next, we add $7$ to both sides of the equation to isolate the term with $n$ on one side. $\newline$ $6n - 7 + 7 = \frac{9}{4} + 7$ $\newline$ $6n = \frac{9}{4} + \frac{28}{4}$ $\newline$ $6n = \frac{37}{4}$
Find Value of n: To find the value of $n$ , we divide both sides of the equation by $6$ . $n = \frac{37}{4} / 6$ $n = \frac{37}{4} \times \frac{1}{6}$ $n = \frac{37}{24}$
Find Value of $2n-2$ : Now that we have the value of $n$ , we can find the value of $2n-2$ . $2n - 2 = 2\times\frac{37}{24} - 2 = \frac{74}{24} - \frac{48}{24} = \frac{26}{24} = \frac{13}{12}$