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

Explanation:

Step1: Apply limit - sum/difference property

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

Step2: Apply limit - constant - multiple property

$\lim_{x\rightarrow a}(cf(x))=c\lim_{x\rightarrow a}f(x)$. 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: Evaluate $\lim_{x\rightarrow9}(x)$

By the property $\lim_{x\rightarrow a}x=a$, when $a = 9$, $\lim_{x\rightarrow9}(x)=9$. Then $3\lim_{x\rightarrow9}(x)=3\times9 = 27$.

Step4: Calculate the final result

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

Answer:

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