Mister Exam
0,4x+16/5>/0 inequation
The solution
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2*x 16 --- + -- > 0 5 5
$$\frac{2 x}{5} + \frac{16}{5} > 0$$
2*x/5 + 16/5 > 0
Detail solution
Given the inequality:
$$\frac{2 x}{5} + \frac{16}{5} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x}{5} + \frac{16}{5} = 0$$
Solve:
Given the linear equation:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$\frac{2 x}{5} = - \frac{16}{5}$$
Divide both parts of the equation by 2/5
$$x_{1} = -8$$
$$x_{1} = -8$$
This roots
$$x_{1} = -8$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-8 + - \frac{1}{10}$$
=
$$- \frac{81}{10}$$
substitute to the expression
$$\frac{2 x}{5} + \frac{16}{5} > 0$$
$$\frac{\left(-81\right) 2}{5 \cdot 10} + \frac{16}{5} > 0$$
Then
$$x < -8$$
no execute
the solution of our inequality is:
$$x > -8$$
$$\frac{2 x}{5} + \frac{16}{5} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x}{5} + \frac{16}{5} = 0$$
Solve:
Given the linear equation:
(2/5)*x+16/5 = 0
Expand brackets in the left part
2/5x+16/5 = 0
Move free summands (without x)
from left part to right part, we given:
$$\frac{2 x}{5} = - \frac{16}{5}$$
Divide both parts of the equation by 2/5
x = -16/5 / (2/5)
$$x_{1} = -8$$
$$x_{1} = -8$$
This roots
$$x_{1} = -8$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-8 + - \frac{1}{10}$$
=
$$- \frac{81}{10}$$
substitute to the expression
$$\frac{2 x}{5} + \frac{16}{5} > 0$$
$$\frac{\left(-81\right) 2}{5 \cdot 10} + \frac{16}{5} > 0$$
-1/25 > 0
Then
$$x < -8$$
no execute
the solution of our inequality is:
$$x > -8$$
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