How do you solve $\frac{x}{x + 2} \geq 2$ $x/(x+2)>=2$ ?

Question

How do I solve the rational inequality $\frac{x - 4}{x + 5} < 4$ $(x-4)/(x+5)<4$ using a TI-84?
How do I solve the rational inequality $\frac{x + 10}{3 x - 2} \leq 3$ $(x+10)/(3x-2)<=3$ using a TI-84?
How do I solve the rational inequality $\frac{x + 2}{2 x + 1} > 5$ $(x+2)/(2x+1)>5$ using a TI-84?
How do I solve the rational inequality $\frac{3 x - 2}{x + 2} \leq \frac{1}{3}$ $(3x-2)/(x+2)<=1/3$ using a TI-83?
How do I solve the rational inequality $\frac{x^{2} - 1}{x + 1} < 2$ $(x^2-1)/(x+1)<2$ using a TI-83?
How do I solve the rational inequality $\frac{x^{2} - x - 6}{x + 2} \leq - 3$ $(x^2-x-6)/(x+2)<=-3$ using a TI-83?
How do you solve rational inequalities?
How do you solve the inequality $\frac{x^{2} - 2 x - 24}{x^{2} - 8 x - 20} \geq 0$ $(x^2-2x-24)/(x^2-8x-20)>=0$ ?
How do you solve the inequality $x^{3} - x^{2} - 6 x > 0$ $x^3-x^2-6x>0$ ?
How do you solve $\frac{16 - x^{2}}{x^{2} - 9} \geq 0$ $(16-x^2)/(x^2-9)>=0$ ?

2117 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-29T09:15:42

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

i.e. $x (x + 2) \geq 2 {(x + 2)}^{2}$ $x(x + 2) >= 2(x + 2)^2$

so, $2 {(x + 2)}^{2} - x (x + 2) \leq 0$ $2(x + 2)^2 - x(x + 2) <= 0$

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

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

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

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

:)>

How do you solve xx+2≥2x/(x+2)>=2?