Question

Solve the compound inequality and graph the solutions.-5<<*>12<-X - 12<-24The solutions to the compound inequality aare

Answer 1

The solutions for the compound inequality are (-8,4) or -8 < x < 4

To solve this, lets divide the inequality in two cases:

`\begin{gathered} (x-12)/(4)<-2 \\ or \\ (x-12)/(4)>-5 \end{gathered}`

Then let's solve each separeately:

`\begin{gathered} (x-12)/(4)<-2 \\ x-12<(-2)\cdot4 \\ x=12-8 \\ x=4 \end{gathered}`

Now for the second part:

`\begin{gathered} (x-12)/(4)>-5 \\ x-12>(-5)\cdot4 \\ x>-20+12 \\ x>-8 \end{gathered}`

The the solutions are all x that are bigger than -8 and smaller than 4. We can write this like x = (-8,4) or -8< x < 4