Question

Consider the following compound inequality. X-3<-9 or x+2_>1A) Solve the inequality for x.B) Graph the compound inequalityC) Enter the solution in interval notation.

Answer 1

a) We must solve the following compound inequality:

$x-3<-9\text{ or }x+2\ge1.$

1) From the first inequality we have:

$\begin{gathered} x-3<-9, \\ x<-9+3, \\ x<-6. \end{gathered}$

2) From the second inequality we have:

$\begin{gathered} x+2\ge1, \\ x\ge1-2, \\ x\ge-1. \end{gathered}$

So we have that the compound inequality is equivalent to:

$x<-6\text{ or }x\ge-1.$

Which can be written as:

$x<-6,x\ge-1$

b) Graph of the compound inequality:

Answer

a. x < -6, x ≥ -1

b. Graph