Step-by-step explanation:
As Serena will make the b team if she scores within 8 points of the team average of 92.
As she scores within 8 points and the team average is 6.
So,
the inequality involving absolute value becomes
[tex]\left|x-92\right|\le \:8[/tex]
Lets solve it
As
[tex]\left|x-92\right|\le \:8[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a[/tex]
[tex]-8\le \:x-92\le \:8[/tex]
[tex]x-92\ge \:-8\quad \mathrm{and}\quad \:x-92\le \:8[/tex]
[tex]\mathrm{Combine\:the\:intervals}[/tex]
[tex]x\ge \:84\quad \mathrm{and}\quad \:x\le \:100[/tex]
[tex]Merge\:Overlapping\:Intervals[/tex]
[tex]84\le \:x\le \:100[/tex]
The solution graph is also attached below.
Keywords: inequality, inequality involving absolute value
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