Confusion about absolute

[Loki123]

Welcome to another "I got the correct answer, but at what cost?"...
First two pictures are my work, second is the solution with the red writing being my comments. The problem is that where I put <, they put <=
I thought when solving absolute you use => and <? Why is it different here? I also used an app to solve this for me and It did the same as I did...could it possible be a mistake in the solution?

 

[Loki123]

i means and in my language

 

[Dr.Peterson]

You'd have to ask the author why they chose to do what they did.

But the fact is, you can include the boundary points in either part of a piecewise definition for an absolute value, and it doesn't hurt to include it in both (though that is not usual). Nothing is lost, because wherever that point (e.g. the 5) is taken, the result will be the same; so they got it as a solution twice. (This is not true for piecewise-defined functions in general, which may not be continuous, but is true for absolute values.)

 

[Loki123]

You'd have to ask the author why they chose to do what they did.

But the fact is, you can include the boundary points in either part of a piecewise definition for an absolute value, and it doesn't hurt to include it in both (though that is not usual). Nothing is lost, because wherever that point (e.g. the 5) is taken, the result will be the same; so they got it as a solution twice. (This is not true for piecewise-defined functions in general, which may not be continuous, but is true for absolute values.)

Thank you!