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$Simplify the expression. Write your answers using integers or improper fractions. (1)/(2)((3)/(2)q-5q-5)-3q Answer:$

Simplify the expression. Write your answers using integers or improper fractions. $\newline$ $\frac{1}{2}\left(\frac{3}{2} q-5 q-5\right)-3 q$ $\newline$ Answer:

Full solution

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

\newline

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

\newline

Answer:

Write Expression: Write down the expression to be simplified. $\newline$ $(\frac{1}{2})((\frac{3}{2})q - 5q - 5) - 3q$
Distribute $(1/2)$ : Distribute the $(1/2)$ across the terms inside the parentheses. $\newline$ $(1/2)(3/2)q - (1/2)(5q) - (1/2)(5) - 3q$
Simplify Each Term: Simplify each term. $\frac{3}{4}q - \frac{5}{2}q - \frac{5}{2} - 3q$
Combine Like Terms: Combine like terms. To combine the terms with $q$ , we need a common denominator. The common denominator for $4$ and $2$ is $4$ . $\newline$ $\frac{3}{4}q - \frac{10}{4}q - \frac{5}{2} - 3q$
Combine Q Terms: Combine the q terms. $\newline$ $(\frac{3}{4})q - (\frac{10}{4})q$ is $(-\frac{7}{4})q$ . $\newline$ Now we need to convert $-3q$ to a fraction with a denominator of $4$ to combine it with $(-\frac{7}{4})q$ . $\newline$ $-3q$ is the same as $(-\frac{12}{4})q$ . $\newline$ $(-\frac{7}{4})q - (\frac{12}{4})q$ is $(-\frac{5}{2})$
Combine Q Terms: Combine the q terms with a common denominator. $\newline$ $(-\frac{7}{4})q - (\frac{12}{4})q$ is $(-\frac{19}{4})q$ . $\newline$ Now we have $(-\frac{19}{4})q - (\frac{5}{2})$ .
Convert to Fraction: Convert $(\frac{5}{2})$ to a fraction with a denominator of $4$ to combine it with $(-\frac{19}{4})q$ . $\newline$ $(\frac{5}{2})$ is the same as $(\frac{10}{4})$ . $\newline$ $(-\frac{19}{4})q - (\frac{10}{4})$
Combine Constant Terms: Combine the constant terms. $(-\frac{19}{4})q - (\frac{10}{4})$ is the simplified expression.