Mister Exam
(abs((x+2)/(-x-1)))<1 inequation
The solution
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|x + 2 | |------| < 1 |-x - 1|
$$\left|{\frac{x + 2}{- x - 1}}\right| < 1$$
Abs((x + 2)/(-x - 1)) < 1
Detail solution
Given the inequality:
$$\left|{\frac{x + 2}{- x - 1}}\right| < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\frac{x + 2}{- x - 1}}\right| = 1$$
Solve:
$$x_{1} = -1.5$$
$$x_{1} = -1.5$$
This roots
$$x_{1} = -1.5$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-1.5 + - \frac{1}{10}$$
=
$$-1.6$$
substitute to the expression
$$\left|{\frac{x + 2}{- x - 1}}\right| < 1$$
$$\left|{\frac{-1.6 + 2}{-1 - -1.6}}\right| < 1$$
the solution of our inequality is:
$$x < -1.5$$
$$\left|{\frac{x + 2}{- x - 1}}\right| < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\frac{x + 2}{- x - 1}}\right| = 1$$
Solve:
$$x_{1} = -1.5$$
$$x_{1} = -1.5$$
This roots
$$x_{1} = -1.5$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-1.5 + - \frac{1}{10}$$
=
$$-1.6$$
substitute to the expression
$$\left|{\frac{x + 2}{- x - 1}}\right| < 1$$
$$\left|{\frac{-1.6 + 2}{-1 - -1.6}}\right| < 1$$
0.666666666666666 < 1
the solution of our inequality is:
$$x < -1.5$$
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Solving inequality on a graph
Rapid solution
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And(-oo < x, x < -3/2)
$$-\infty < x \wedge x < - \frac{3}{2}$$
(-oo < x)∧(x < -3/2)
Rapid solution 2
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(-oo, -3/2)
$$x\ in\ \left(-\infty, - \frac{3}{2}\right)$$
x in Interval.open(-oo, -3/2)