Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.

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-\frac{1}{2} v-3\left(-3 v-\frac{5}{2}\right)

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Answer:

Distribute negative sign: Distribute the negative sign inside the parentheses. $\newline$ We have the expression $-\left(\frac{1}{2}\right)v - 3(-3v - \left(\frac{5}{2}\right))$ . First, we distribute the $-3$ across the parentheses to both $-3v$ and $-\frac{5}{2}$ . $\newline$ $-3 \times -3v = 9v$ $\newline$ $-3 \times -\left(\frac{5}{2}\right) = \frac{15}{2}$
Combine distributed terms: Combine the distributed terms with the rest of the expression. $\newline$ Now we combine the terms from the distribution with the initial $-\frac{1}{2}v$ . $\newline$ $-\frac{1}{2}v + 9v + \frac{15}{2}$
Combine like terms: Combine like terms. $\newline$ We need to combine the $v$ terms. To do this, we need a common denominator. The common denominator for $\frac{1}{2}$ and $9$ (which is $\frac{9}{1}$ ) is $2$ . $\newline$ $-\left(\frac{1}{2}\right)v$ is the same as $-\frac{1}{2}v$ . $\newline$ $9v$ is the same as $\frac{18}{2}v$ . $\newline$ Now we add $-\frac{1}{2}v$ and $\frac{18}{2}v$ . $\newline$ $\frac{1}{2}$ $1$
Write final expression: Write the final simplified expression. $\newline$ Now we have the $v$ term and the constant term. The final expression is: $\newline$ $(\frac{17}{2})v + \frac{15}{2}$