use properties of limits to find the indicated limit. it may be necessary to rewrite the expression before…

Explanation:

Step1: Apply limit - sum/difference rule

$\lim_{x\rightarrow a}(f(x)-g(x))=\lim_{x\rightarrow a}f(x)-\lim_{x\rightarrow a}g(x)$. So, $\lim_{x\rightarrow9}(3x - 2)=\lim_{x\rightarrow9}(3x)-\lim_{x\rightarrow9}(2)$.

Step2: Apply constant - multiple rule

$\lim_{x\rightarrow a}(cf(x))=c\lim_{x\rightarrow a}f(x)$. Here, $\lim_{x\rightarrow9}(3x)=3\lim_{x\rightarrow9}(x)$. And $\lim_{x\rightarrow9}(2) = 2$ (since the limit of a constant function $y = c$ as $x\rightarrow a$ is $c$).

Step3: Apply direct - substitution for $\lim_{x\rightarrow9}(x)$

We know that $\lim_{x\rightarrow a}x=a$. So, $3\lim_{x\rightarrow9}(x)=3\times9 = 27$.

Step4: Calculate the final result

$3\lim_{x\rightarrow9}(x)-\lim_{x\rightarrow9}(2)=27 - 2=25$.

Answer:

A. $\lim_{x\rightarrow9}(3x - 2)=25$