Mister Exam
(2*x+5)/|2+x|<1 inequation
The solution
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[src]
2*x + 5 ------- < 1 |2 + x|
$$\frac{2 x + 5}{\left|{x + 2}\right|} < 1$$
(2*x + 5)/|x + 2| < 1
Detail solution
Given the inequality:
$$\frac{2 x + 5}{\left|{x + 2}\right|} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x + 5}{\left|{x + 2}\right|} = 1$$
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
$$\frac{0 \cdot 2 + 5}{\left|{2}\right|} < 1$$
but
so the inequality has no solutions
$$\frac{2 x + 5}{\left|{x + 2}\right|} < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x + 5}{\left|{x + 2}\right|} = 1$$
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
$$\frac{0 \cdot 2 + 5}{\left|{2}\right|} < 1$$
5/2 < 1
but
5/2 > 1
so the inequality has no solutions
Solving inequality on a graph
Rapid solution
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And(-oo < x, x < -7/3)
$$-\infty < x \wedge x < - \frac{7}{3}$$
(-oo < x)∧(x < -7/3)
Rapid solution 2
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(-oo, -7/3)
$$x\ in\ \left(-\infty, - \frac{7}{3}\right)$$
x in Interval.open(-oo, -7/3)