Chapter 4.9, Problem 8WE

To determine

To find and graph: The given equation of each inequality.

Answer to Problem 8WE

The solution set of the given inequality is,

  $\left\{s:s<4\text{ or }s<-4\right\}$

Explanation of Solution

Given information:

The equation is given as: $3s^2\ge 48$

Calculation:

The solution set of the given equation can be find as:

  $\begin{array}{l}3s^2<48\text{ write original eqaution}\text{.}\\ \left(s^2-4^2\right)\text{<0 factor the polynomial and make one side zero}\text{.}\\ \left(s+4\right)\left(s-4\right)<0\end{array}$

The sign of the product $\left(s+4\right)\left(s-4\right)<0$ is determined by the number of negative factors. When exactly one or exactly three factors are negative, the product is negative. When no factors or exactly 2 factors are negative, the product is positive.

  

The solution set of the given inequality is $\left\{s:s<4\text{ or y<}-4\right\}$