Chapter 7.6, Problem 1PE

a)

To determine

To fill in the blanks of the given statement “An inequality of the form $a{x}^2+bx+c>0\left(a\ne 0\right)$ is an example of a ______ inequality”.

b)

To determine

To fill in the blanks of the given statement “The boundary points of an inequality consist of the real ______ to the related equation and the points where the inequality is ______ ”.

c)

To determine

To fill in the blanks of the given statement “In solving an inequality by using ______ method, a point is selected from each interval formed by the boundary points and substituted into the original inequality”.

d)

To determine

The appropriate choice for the given statement.

e)

To determine

To fill in the blanks of the given statement “The inequality $\frac{4}{x+7}>0$ is an example of a ______ inequality.”

f)

To determine

To fill in the blanks of the given statement “The solution set to a rational inequality must exclude all the values that make the ______ equal to zero for any rational expression in the original inequality.”

g)

To determine

To fill in the blanks of the given statement “The solution set to the inequality ${(x+3)}^2\le -4$ is______, whereas the solution set to the inequality ${(x+3)}^2\ge -4$ is______”.

h)

To determine

The appropriate choice for the given statement.