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

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Answer 1 · 2017-07-29T09:15:42

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

i.e. $x(x + 2) >= 2(x + 2)^2$

so, $2(x + 2)^2 - x(x + 2) <= 0$

=> $(x + 2)[2(x + 2) - x] <= 0$

i.e. $(x + 2)(x + 4) <= 0$

Hence, $-4 <= x < -2$

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

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