Answer:
Im Pretty Sure This Is The Answer f = -1
Step-by-step explanation:
[tex]Solution, solve\:for\:f,\:\left|f-6\right|=\left|f+8\right|\quad :\quad f=-1[/tex]
[tex]Steps:[/tex]
[tex]\left|f-6\right|=\left|f+8\right|[/tex]
[tex]\mathrm{Test\:each\:absolute\:for\:its\:positive\:and\:negative\:ranges},\\f-6\ge \:0\:\mathrm{for}\:f\ge \:6,\:\quad \mathrm{therefore\:for}\:f\ge \:6\quad \left|f-6\right|=f-6,\\f-6<0\:\mathrm{for}\:f<6,\:\quad \mathrm{therefore\:for}\:f<6\quad \left|f-6\right|=-\left(f-6\right),\\f+8\ge \:0\:\mathrm{for}\:f\ge \:-8,\:\quad \mathrm{therefore\:for}\:f\ge \:-8\quad \left|f+8\right|=f+8,\\f+8<0\:\mathrm{for}\:f<-8,\:\quad \mathrm{therefore\:for}\:f<-8\quad \left|f+8\right|=-\left(f+8\right)[/tex]
[tex]\mathrm{Evaluate\:the\:expression\:in\:the\:following\:ranges:}\\f<-8,\:-8\le \:f<6,\:f\ge \:6[/tex]
[tex]\mathrm{For:}\:f<-8,\\\mathrm{Replace:}\:\left|f-6\right|\:\mathrm{with}\:-\left(f-6\right),\\\mathrm{Replace:}\:\left|f+8\right|\:\mathrm{with}\:-\left(f+8\right),\\-\left(f-6\right)=\left(-\left(f+8\right)\right)\quad :\quad \mathrm{No\:Solution\:for\:f\in \mathbb{R}}[/tex]
[tex]\mathrm{For:}\:-8\le \:f<6,\\\mathrm{Replace:}\:\left|f-6\right|\:\mathrm{with}\:-\left(f-6\right),\\\mathrm{Replace:}\:\left|f+8\right|\:\mathrm{with}\:\left(f+8\right),\\-\left(f-6\right)=\left(f+8\right)\quad :\quad f=-1[/tex]
[tex]\mathrm{For:}\:f\ge \:6,\\\mathrm{Replace:}\:\left|f-6\right|\:\mathrm{with}\:\left(f-6\right),\\\mathrm{Replace:}\:\left|f+8\right|\:\mathrm{with}\:\left(f+8\right),\\f-6=\left(f+8\right)\quad :\quad \mathrm{No\:Solution\:for\:f\in \mathbb{R}}[/tex]
[tex]\mathrm{Combine\:the\:ranges}, \\\left(-8\le \:f<6\quad \mathrm{and}\quad \:f=-1\right), \\f=-1[/tex]
[tex]\mathrm{The\:Correct\:Answer\:is\:f=-1}[/tex]
[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]
[tex]\mathrm{-Austint1414}[/tex]
