Which inequality is equivalent to |X-41<9?

0 - 9 > x-4<9

09 O X - 4<-9 or x - 4< 9

O x-4> - 9 or x - 4<9

x - 4 > - 9 or x - 4 < 9

Step-by-step explanation:

Let's see the definition of absolute value inequality.

i) If lxl < b, then - b < x < b

ii) If lxl > b, then x > b or x < - b

We are given the inequality lx - 4l<9

Here we have to use the first case.

Using the above definition of inequality, we can write the given inequality as follows:

-9 < (x - 4) < 9

So the third option is correct.

x - 4 > - 9 or x - 4 < 9