Answer:
something like this?
[tex]\left \{ {{x-4<9} \atop {-(x-4) < 9} \right.[/tex]
the top one is valid when x-4 >0
the bottom one is valid when x-4<0
Step-by-step explanation:
absolute value |x-4|
means that in case x-4 is negative, we will use -(x-4)
if it's positive we use x-4
let's find the solution (where the original inequality is true)
negative case:
-(x-4)<9 -x+4 < 9 -x < 5 x>-5
positive case:
x-4 < 9 x < 13
to satisfy both conditions -5 < x < 13
