Mister Exam
12÷(4+3x-x^2)<=0 inequation
The solution
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[src]
12
------------ <= 0
2
4 + 3*x - x
$$\frac{12}{- x^{2} + \left(3 x + 4\right)} \leq 0$$
12/(-x^2 + 3*x + 4) <= 0
Detail solution
Given the inequality:
$$\frac{12}{- x^{2} + \left(3 x + 4\right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{12}{- x^{2} + \left(3 x + 4\right)} = 0$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
$$\frac{12}{- 0^{2} + \left(0 \cdot 3 + 4\right)} \leq 0$$
but
so the inequality has no solutions
$$\frac{12}{- x^{2} + \left(3 x + 4\right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{12}{- x^{2} + \left(3 x + 4\right)} = 0$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0
$$\frac{12}{- 0^{2} + \left(0 \cdot 3 + 4\right)} \leq 0$$
3 <= 0
but
3 >= 0
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
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Or(And(4 < x, x < oo), x < -1)
$$\left(4 < x \wedge x < \infty\right) \vee x < -1$$
(x < -1)∨((4 < x)∧(x < oo))
Rapid solution 2
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(-oo, -1) U (4, oo)
$$x\ in\ \left(-\infty, -1\right) \cup \left(4, \infty\right)$$
x in Union(Interval.open(-oo, -1), Interval.open(4, oo))