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!