91Ó°ÊÓ

The solution of the given inequality$\left|f−9\right|â‰\yen 2$ is:

Case 1:$f−9$ is non-negative.

$\begin{array}{c}f−9â‰\yen 2\\ f−9+9â‰\yen 2+9\\ fâ‰\yen 11\\ f∈\left[11,∞\right)\end{array}$

Case 2:$f−9$ is negative.

$\begin{array}{c}−\left(f−9\right)â‰\yen 2\\ \left(−1\right)\left(−\left(f−9\right)\right)≤\left(−1\right)\left(2\right)\\ f−9≤−2\\ f−9+9≤−2+9\\ f≤7\\ f∈\left(−∞,7\right]\end{array}$

The solution of the inequality $\left|x\right|â‰\yen a$is $x≤−a$or $xâ‰\yen a$.

That implies the solution of the inequality$\left|x\right|â‰\yen a$ is the union of the solutions of the inequalities$x≤−a$ and $xâ‰\yen a$.

Find the union of the solutions of the inequalities$f−9â‰\yen 2$ and$f−9≤−2$ to find the solution of the inequality $\left|f−9\right|â‰\yen 2$.

The union of the solutions of the inequalities$f−9â‰\yen 2$ and$f−9≤−2$ is:

$f∈\left(−∞,7\right]∪\left[11,∞\right)$

Therefore, the solution of the inequality$\left|f−9\right|â‰\yen 2$ is $f∈\left(−∞,7\right]∪\left[11,∞\right)$.

The graph of the solution set which is$f∈\left(−∞,7\right]∪\left[11,∞\right)$ is: