Question

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

Answer 1

Answer:

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