Answer:
All real numbers
Step-by-step explanation:
Assuming it's positive:
2>-(x-8)/5 -3/5
8>-(x-8)
8>-x+8
-x<0
x>0
Assuming it's negative:
2>(x-8)/5 + 3/5
10>x-5
15>x
x<15
Since these together cover all numbers, then the inequality must cover all real numbers. You can check this by realizing that whatever is in the absolute value, the negative of that will be smaller than 2. Hope this helped!
The set of solutions for absolute value inequality is [tex]-5 < x < 15[/tex]
To understand more, check below explanation.
The absolute value inequality is,
[tex]2 > -|\frac{x-8}{5}+\frac{3}{5} |\\\\2 > -|\frac{x-5}{5} |[/tex]
First assuming it is positive:
[tex]2 > -\frac{x-5}{5} \\\\10 > -x+5\\\\x > 5-10\\\\x > -5[/tex]
Assuming it is negative:
[tex]2 > \frac{x-5}{5} \\\\x-5 < 10\\\\x < 15[/tex]
Therefore, the set of solutions for absolute value inequality is [tex]-5 < x < 15[/tex]
Learn more about the inequality here:
https://brainly.com/question/24372553
