Question

REASONING If the solution set of a polynomial inequality is (−3, 3), what will be the solution set if the inequality symbol is reversed? Explain your reasoning.

Answer 1

Answer:  The new solution set is  $(-\infty,-3)\cup(3,\infty).$

Step-by-step explanation:  Given that the solution set of a polynomial inequality is (-3, 3).

We are to find the solution set if the inequality symbol is reversed.

Let x denotes the unknown variable in the original inequality.

Then, according to the given information, we can write

$x\in (-3,3)\\\\\Rightarrow -3$

Now, if we reverse the sign of the inequality, then the value of x will be

$x3.$

This new solution set can be written as

$x\in(-\infty,-3)\cup(3,\infty).$

Thus, the new solution set is  $(-\infty,-3)\cup(3,\infty).$