Question

Consider the following compound inequality.{x | x + 3 <-3 or x + 5 > 9}Step 1 of 2: Write the solution using interval notation.Answer

Answer 1

We are given the following compound inequality

$\mleft\lbrace x\mright|x+3<-3\; or\; x+5>9\}$

Let us solve the compound inequality.

$x+3<-3$

Subtract 3 from each side of the inequality

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

Now, let us solve the other part of the inequality

$x+5>9_{}$

Subtract 5 from each side of the inequality

$\begin{gathered} x+5-5>9-5 \\ x>4 \end{gathered}$

So, the solution of the compound inequality is x less than -6 or x is greater than 4.

$x<-6\; or\; x>4$

The solution in interval notation is

$interval\; notation\colon(-\infty,-6)\cup(4,\infty)$