Chapter 4.9, Problem 7WE

To determine

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

Answer to Problem 7WE

The solution set of the given inequality is,

  $\left\{y:y\ge 3\text{ or y}\ge -3\right\}$

Explanation of Solution

Given information:

The equation is given as: $4y^2\ge 36$

Calculation:

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

  $\begin{array}{l}4y^2\ge 36\text{ write original eqaution}\text{.}\\ 4\left(y^2-9\right)\ge \text{0 factor the polynomial and make one side zero}\text{.}\\ \left(y+3\right)\left(y-3\right)\ge 0\end{array}$

The sign of the product $\left(y+3\right)\left(y-3\right)\ge 0$ 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 $\left\{y:y\ge 3\text{ or y}\ge -3\right\}$