How do solve $\frac{x (4 - x)}{x + 2} \geq 0$ $(x(4-x))/(x+2)>=0$ graphically?

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 $\frac{16 - x^{2}}{x^{2} - 9} \geq 0$ $(16-x^2)/(x^2-9)>=0$ ?

1644 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-06T09:44:15

The solution is $x \in (- \infty, - 2) \cup [0, 4]$ $x in (-oo,-2) uu [0, 4]$

First, plot the graph

graph{(x(4-x))/(x+2) [-18.02, 18.04, -9.01, 9.01]}

The function is

$\frac{x (4 - x)}{x + 2} \geq 0$ $(x(4-x))/(x+2)>=0$

And look where the function is $\geq 0$ $>=0$

The solution is

$x \in (- \infty, - 2) \cup [0, 4]$ $x in (-oo,-2) uu [0, 4]$

How do solve x(4−x)x+2≥0(x(4-x))/(x+2)>=0 graphically?