Question

Which inequivalnet is equivalent to |x-4|<9

Answer 1

Answer:

something like this?

$\left \{ {{x-4$  

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