I can´t solve any inequalities with absolute value

[solemn thorn]

I started going to the university, but one of the first math topics of the first units is this, I need someone who could explain to me how can I solve this. I find this very difficult. My teacher used a methood in which he drew a table with numbers.

[solemn thorn]

I need to learn this because on thursday i´m having an important exam

[digital hemlock]

so when you remove the absolute value sign, the inside expression can either be the same or the inside times -1. so then we just split it up to 2 cases to evaluate

[solemn thorn]

my teacher did a table similar to this one when he was explaining the example

[gray hamlet]

Basically the absolute function makes everything positive, in essence let’s say I input x = -1 into y = |x|, it would be y = 1.

And because the absolute function for linear graphs is just a v-shaped graph