Question

slove the inequality:|x+2| +x>=0

Answer 1

The inequality can be decomposed into two inequalities.

$-(x+2)+x\ge0$

and

$(x+2)+x\ge0$

This is because |x+2| = |-(x+2)|.

Let us first solve the first inequality by first simplifying it

$\begin{gathered} -x-2+x\ge0 \\ -2\ge0 \end{gathered}$

it has no solutions.

Let us now turn to the second inequality which simplifies to

$2x+2\ge0$

subtracting 2 from both sides and then dividing both sides by 2 gives

$x\ge-1$

which is our answer!