Mister Exam
x-2x>=0 inequation
The solution
Detail solution
Given the inequality:
$$- 2 x + x \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- 2 x + x = 0$$
Solve:
Given the linear equation:
Looking for similar summands in the left part:
Divide both parts of the equation by -1
$$x_{1} = 0$$
$$x_{1} = 0$$
This roots
$$x_{1} = 0$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$- 2 x + x \geq 0$$
$$- \frac{1}{10} - \frac{\left(-1\right) 2}{10} \geq 0$$
the solution of our inequality is:
$$x \leq 0$$
$$- 2 x + x \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- 2 x + x = 0$$
Solve:
Given the linear equation:
x-2*x = 0
Looking for similar summands in the left part:
-x = 0
Divide both parts of the equation by -1
x = 0 / (-1)
$$x_{1} = 0$$
$$x_{1} = 0$$
This roots
$$x_{1} = 0$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$- 2 x + x \geq 0$$
$$- \frac{1}{10} - \frac{\left(-1\right) 2}{10} \geq 0$$
1/10 >= 0
the solution of our inequality is:
$$x \leq 0$$
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