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

Aug 21, 2016

The inequation has not solutions.

Explanation:

$\left\mid x + 1 \right\mid + x + 1 < - 1$ or

$\left\mid x + 1 \right\mid + x + 1 + 1 < 0$

now, for $x \ne - 1$

$1 + \frac{x + 1}{\left\mid x + 1 \right\mid} + \frac{1}{\left\mid x + 1 \right\mid} < 0$ but

$\frac{x + 1}{\left\mid x + 1 \right\mid} = \pm 1$ so

$1 \pm 1 + \frac{1}{\left\mid x + 1 \right\mid} < 0$ which is impossible.

So the inequation has not solutions.

Aug 21, 2016

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,

$x < - \frac{3}{2} < - 1$. And so, this case is ruled out.

Similarly,$| x + 1 | = - \left(x + 1\right)$, for x $< = - 1.$. If so,

$- \left(x + 1\right) + \left(x + 1\right) = 0 > - 1$.

And so, this case is also ruled out.