Full solution

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

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-3(-f-3 f+2)+\frac{9}{5} f

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Answer:

Distribute Terms: Distribute $-3$ to each term inside the parentheses. $\newline$ We have the expression $-3(-f - 3f + 2)$ . Distribute $-3$ to each term inside the parentheses. $\newline$ $-3 \times -f = 3f$ $\newline$ $-3 \times -3f = 9f$ $\newline$ $-3 \times 2 = -6$ $\newline$ So, the expression becomes $3f + 9f - 6$ .
Combine Like Terms: Combine like terms. $\newline$ We have $3f + 9f$ from the previous step. Combine these like terms. $\newline$ $3f + 9f = 12f$ $\newline$ So, the expression now is $12f - 6$ .
Add Fraction Part: Add the fraction part of the expression. $\newline$ We have the fraction $(\frac{9}{5})f$ to add to our current expression $12f - 6$ . $\newline$ Since $12f$ is the same as $(\frac{60}{5})f$ , we can write the expression as $(\frac{60}{5})f - 6 + (\frac{9}{5})f$ .
Combine Like Terms with Fractions: Combine like terms with fractions. $\newline$ We have $(\frac{60}{5})f + (\frac{9}{5})f$ from the previous step. Combine these like terms. $\newline$ $(\frac{60}{5})f + (\frac{9}{5})f = (\frac{69}{5})f$ $\newline$ So, the expression now is $(\frac{69}{5})f - 6$ .
Final Simplified Expression: The expression is already simplified. $\newline$ The final simplified expression is $(\frac{69}{5})f - 6$ , which is in terms of integers and improper fractions.