Question

Your friend says that the absolute value equation |3x+8|−9=−5 has no solution because the constant on the right side of the equation is negative. Is your friend correct? Explain.

Answer 1

`Solution, solve\:for\:x,\:\left|3x+8\right|-9=-5\quad :\quad x=-4\quad \mathrm{or}\quad \:x=-(4)/(3)`

`Steps:`

`\left|3x+8\right|-9=-5`

`\mathrm{Add\:}9\mathrm{\:to\:both\:sides},\\\left|3x+8\right|-9+9=-5+9`

`\mathrm{Simplify},\\\left|3x+8\right|=4`

`|f\left(x\right)|=a\quad \Rightarrow \:f\left(x\right)=-a\quad \mathrm{or}\quad \:f\left(x\right)=a,\\3x+8=-4\quad \quad \mathrm{or}\quad \:\quad \:3x+8=4`

`3x+8=-4,\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides},\\3x+8-8=-4-8,\\\mathrm{Simplify},\\3x=-12,\\\mathrm{Divide\:both\:sides\:by\:}3,\\(3x)/(3)=(-12)/(3),\\\mathrm{Simplify},\\x=-4`

`3x+8=4,\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides},\\3x+8-8=4-8,\\\mathrm{Simplify},\\3x=-4,\\\mathrm{Divide\:both\:sides\:by\:}3,\\(3x)/(3)=(-4)/(3),\\\mathrm{Simplify},\\x=-(4)/(3)`

`Combine\:the\:ranges,\\x=-4\quad \mathrm{or}\quad \:x=-(4)/(3)`

`\mathrm{The\:Correct\:Answer\:is\:No\:They\:Are\:Not\:Correct}`

`\mathrm{Hope\:This\:Helps!!!}`

`\mathrm{-Austint1414}`