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<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).`