Question

Consider the following compound inequality.x 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)`