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.

Question

asked Jul 4, 2020 39.8k views

1 Answer

Aramusss · Answer 1 · 2020-07-10T10:48:44+0000

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

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

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

$x<-3~~~\textup{and}~~~x>3.$

This new solution set can be written as

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

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