Question

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

Answer 1

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.

Answer 2

`Solution, \left|6+y\right|=2\quad :\quad y=-8\quad \mathrm{or}\quad \:y=-4`

`Steps:`

`|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`

`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`

`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`

`\mathrm{Combine\:the\:ranges}, y=-8\quad \mathrm{or}\quad \:y=-4`

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

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

`\mathrm{-Austint1414}`