(3v+2)-((2)/(3)v-(1)/(4)) Which of the following is equivalent to the given expression? Choose 1 answer: (A) (7)/(3)v+(7)/(4) (B) (7)/(3)v+(9)/(4) (C) 2v^(2)+(1)/(2) (D) 2v^(2)+(7)/(12)v-(1)/(2)

Simplify Expression: First, let's simplify the expression (3v+2)-((2)/(3)v-(1)/(4)). We'll start by distributing the negative sign to the terms inside the second set of parentheses. (3v+2)-((2)/(3)v-(1)/(4)) = 3v + 2 - (2/3)v + 1/4Combine Like Terms: Now, we combine like terms. The v terms are 3v and -(2/3)v, and the constant terms are 2 and 1/4. To combine the v terms: 3v - (2/3)v = (9/3)v - (2/3)v = (7/3)v To combine the constant terms: 2 + 1/4 = (8/4) + (1/4) = (9/4)Final Simplified Expression: So, the simplified expression is (7/3)v + (9/4). This matches answer choice (B).

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(3v+2)-((2)/(3)v-(1)/(4))
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
(7)/(3)v+(7)/(4)
(B)
(7)/(3)v+(9)/(4)
(C)
2v^(2)+(1)/(2)
(D)
2v^(2)+(7)/(12)v-(1)/(2)

$(3 v+2)-\left(\frac{2}{3} v-\frac{1}{4}\right)$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{7}{3} v+\frac{7}{4}$ $\newline$ (B) $\frac{7}{3} v+\frac{9}{4}$ $\newline$ (C) $2 v^{2}+\frac{1}{2}$ $\newline$ (D) $2 v^{2}+\frac{7}{12} v-\frac{1}{2}$

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(3 v+2)-\left(\frac{2}{3} v-\frac{1}{4}\right)

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

\frac{7}{3} v+\frac{7}{4}

\newline

(B)

\frac{7}{3} v+\frac{9}{4}

\newline

(C)

2 v^{2}+\frac{1}{2}

\newline

(D)

2 v^{2}+\frac{7}{12} v-\frac{1}{2}

Simplify Expression: First, let's simplify the expression $(3v+2)-\left(\frac{2}{3}v-\frac{1}{4}\right)$ . We'll start by distributing the negative sign to the terms inside the second set of parentheses. $\newline$ $(3v+2)-\left(\frac{2}{3}v-\frac{1}{4}\right) = 3v + 2 - \frac{2}{3}v + \frac{1}{4}$
Combine Like Terms: Now, we combine like terms. The $v$ terms are $3v$ and $-\left(\frac{2}{3}\right)v$ , and the constant terms are $2$ and $\frac{1}{4}$ . $\newline$ To combine the $v$ terms: $3v - \left(\frac{2}{3}\right)v = \left(\frac{9}{3}\right)v - \left(\frac{2}{3}\right)v = \left(\frac{7}{3}\right)v$ $\newline$ To combine the constant terms: \(2 + \frac{ $1$ }{ $4$ } = \left(\frac{ $8$ }{ $4$ }\right) + \left(\frac{ $1$ }{ $4$ }\right) = \left(\frac{ $9$ }{ $4$ }\right)
Final Simplified Expression: So, the simplified expression is $(\frac{7}{3})v + (\frac{9}{4})$ . This matches answer choice (B).