How do you solve and graph #abs(m+19)<=1#?

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Answer 1 · 2017-04-19T14:07:03

Normally, when we want to solve for #x#, we move everything besides #x# to the other side. But what is the inverse of #abs(color(white)(x+7)#?

Well, the absolute value bars make the value inside of them positive. So, #abs(2)# and #abs(-2)# both equal #2#.

Based on that fact, #abs(m+19)# could be based on two situations: #(m+19)# or #-1(m+19)#. We need to solve for both of these situations:

Situation 1
#m+19<=1#
subtract #19# on both sides
#m<=-18#

Situation 2
#-1(m+19)<=1#
divide by #-1# on both sides
#m+19=-1#

Notice, the sign (#<=#) changed. Whenever we divide by a negative number, the sign switches

subtract by #19# on both sides
#m>=-1-19#
#m>=-20#

So, our two values are #m<=-18# and #m>=-20#. These are the #x-#intercepts

graph{abs(x+19)-1}