Question

1. select all the expressions that show a way to factor the expression $-\frac{6}{5}x + \frac{18}{5}$. $-\frac{6}{5}(x - 3)$ $\frac{6}{5}(-x - 3)$ $-\frac{6}{5}(x + 3)$ $\frac{6}{5}(-x + 3)$ $\frac{6}{5}(x + 3)$

Explanation:

Step1: Analyze the first option

Factor out \(-\frac{6}{5}\) from \(-\frac{6}{5}x+\frac{18}{5}\).
\[
-\frac{6}{5}(x - 3)=-\frac{6}{5}x+\frac{18}{5}
\]
So this option is correct.

Step2: Analyze the second option

Expand \(\frac{6}{5}(-x - 3)\):
\[
\frac{6}{5}(-x - 3)=-\frac{6}{5}x-\frac{18}{5}
eq-\frac{6}{5}x+\frac{18}{5}
\]
So this option is incorrect.

Step3: Analyze the third option

Expand \(-\frac{6}{5}(x + 3)\):
\[
-\frac{6}{5}(x + 3)=-\frac{6}{5}x-\frac{18}{5}
eq-\frac{6}{5}x+\frac{18}{5}
\]
So this option is incorrect.

Step4: Analyze the fourth option

Expand \(\frac{6}{5}(-x + 3)\):
\[
\frac{6}{5}(-x + 3)=-\frac{6}{5}x+\frac{18}{5}
\]
So this option is correct.

Step5: Analyze the fifth option

Expand \(\frac{6}{5}(x + 3)\):
\[
\frac{6}{5}(x + 3)=\frac{6}{5}x+\frac{18}{5}
eq-\frac{6}{5}x+\frac{18}{5}
\]
So this option is incorrect.

Answer:

\(-\frac{6}{5}(x - 3)\), \(\frac{6}{5}(-x + 3)\)