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

2 Answers
Aug 21, 2016

Answer:

The inequation has not solutions.

Explanation:

#abs(x+1)+x+1<-1# or

#abs(x+1)+x+1 +1<0#

now, for #x ne -1#

#1+(x+1)/abs(x+1) + 1/abs(x+1) < 0# but

#(x+1)/abs(x+1) = pm1# so

#1 pm 1 + 1/abs(x+1) < 0# which is impossible.

So the inequation has not solutions.

Aug 21, 2016

Answer:

Invalid inequality. No solution at all.

Explanation:

#|x+1| = x + 1#, for #x > = -1.#. If so, 2x+1 has to be #< -1#,

and for this to happen,

#x < -3/2 < -1#. And so, this case is ruled out.

Similarly,#|x+1| = -(x + 1)#, for x #< = -1.#. If so,

#-(x+1)+(x+1)=0 > -1#.

And so, this case is also ruled out.