What is #|20x| = |4x+16|#?

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Answer 1 · 2016-10-02T05:21:19

#x=(1,-2/3)#

We know that

#color(blue)(|x|=(-x,x)#

So we can split the equation into two

#rarrcolor(orange)(20x=4x+16#

#rarrcolor(violet)(20x=-(4x+16)#

Solve both of the equations

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#rarrcolor(orange)(20x-4x=16#

#rarrcolor(orange)(16x=16#

#rarrcolor(green)(x=16/16=1#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#rarrcolor(violet)(20x=-4x-16)#

#rarrcolor(violet)(20x+4x=-16#

#rarrcolor(violet)(24x=-16#

#rarrcolor(green)(x=-16/24=-2/3#

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