How do you solve and graph #abs(x+1)<0#?

1 Answer
Rhys
Oct 29, 2017

No solutions
graph{abs(x+1) [-10, 10, -5, 5]}

Explanation:

We can note that #|a| >= 0, |a|# is never negative for all real #a#, so hence #|x+1|# is never negative, hence no solutions to #|x+1|<0#.

To sketch this graph, we can consider #y = x+1#
graph{y = x+1 [-10, 10, -5, 5]}

Then as we know #|a| >= 0# for all real a, we just take the graph in the domain where the function is negative, and reflect in the x axis, so for #x<-1# we make possitive, yielding;

graph{|x+1| [-10, 10, -5, 5]}

We can see clearly from this that #|x+1|# is never negative

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