The solutions for the compound inequality are (-8,4) or -8 < x < 4
To solve this, lets divide the inequality in two cases:
[tex]\begin{gathered} \frac{x-12}{4}<-2 \\ or \\ \frac{x-12}{4}>-5 \end{gathered}[/tex]
Then let's solve each separeately:
[tex]\begin{gathered} \frac{x-12}{4}<-2 \\ x-12<(-2)\cdot4 \\ x=12-8 \\ x=4 \end{gathered}[/tex]
Now for the second part:
[tex]\begin{gathered} \frac{x-12}{4}>-5 \\ x-12>(-5)\cdot4 \\ x>-20+12 \\ x>-8 \end{gathered}[/tex]
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
