# How do you solve x/(x+2)>=2?

Jul 29, 2017

We need to multiply both sides by ${\left(x + 2\right)}^{2}$ in order to preserve the inequality sign

i.e. $x \left(x + 2\right) \ge 2 {\left(x + 2\right)}^{2}$

so, $2 {\left(x + 2\right)}^{2} - x \left(x + 2\right) \le 0$

=> $\left(x + 2\right) \left[2 \left(x + 2\right) - x\right] \le 0$

i.e. $\left(x + 2\right) \left(x + 4\right) \le 0$

Hence, $- 4 \le x < - 2$

Note x cannot equal -2 as this is excluded from the domain

:)>