How do you solve #abs(x+5)=4#?

1 Answer
georgef
Jul 22, 2016

You have to use the definition of #|a|#

Explanation:

The definition of #|a|# is:
#a# if #a>=0#
#-a# if #a<=0#

For example, #|5|=5#, #|-5|=5#, and #|0|=0#

So, let break down the problem into two parts:

#|x+5|>=0#; in this case #|x+5|=x+5#, and the equation is #x+5=4#, so #x=-1#

#|x+5|<0#; in this case #|x+5|=-(x+5)=-x-5#, and the equation is #-x-5=4#, so #x=-9#

The solutions are then #x=-1# and #x=-9#

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