Why are there two solutions for the equation |6 + y| = 2? Explain.

[tex]|f\left(y\right)|=a\quad \Rightarrow \:f\left(y\right)=-a\quad \mathrm{or}\quad \:f\left(y\right)=a, 6+y=-2\quad \quad \mathrm{or}\quad \:\quad \:6+y=2[/tex]

[tex]6+y=-2\quad :\quad y=-8,\\6+y=-2,\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}, 6+y-6=-2-6,\\\mathrm{Simplify}, y=-8[/tex]

[tex]6+y=2\quad :\quad y=-4,\\6+y=2,\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides},6+y-6=2-6\\\mathrm{Simplify},y=-4[/tex]

[tex]\mathrm{Combine\:the\:ranges}, y=-8\quad \mathrm{or}\quad \:y=-4[/tex]

[tex]\mathrm{The\:Correct\:Answer\:is\:Because\:of\:the\:absolute\:value,\:It\:could\:be\:Positive\:or\:negative.}[/tex]

[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]

[tex]\mathrm{-Austint1414}[/tex]

20226017 20226017 · Answer 2 · 2020-10-26T19:50:56+01:00

20226017 20226017

26-10-2020

Answer:

Here is what I wrote:

There are two solutions for |6+y|=2, -8 and -4.

This is because |6+(-8)| and |6+(-4)| both equal 2.

The absolute value is the distance to zero on a number line.

If one were to graph the equation there would be a line with two different directions to determine distance from 0.

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