Mister Exam
37,8−6,3x>0 inequation
The solution
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189 63*x --- - ---- > 0 5 10
$$\frac{189}{5} - \frac{63 x}{10} > 0$$
189/5 - 63*x/10 > 0
Detail solution
Given the inequality:
$$\frac{189}{5} - \frac{63 x}{10} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{189}{5} - \frac{63 x}{10} = 0$$
Solve:
Given the linear equation:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$- \frac{63 x}{10} = - \frac{189}{5}$$
Divide both parts of the equation by -63/10
$$x_{1} = 6$$
$$x_{1} = 6$$
This roots
$$x_{1} = 6$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 6$$
=
$$\frac{59}{10}$$
substitute to the expression
$$\frac{189}{5} - \frac{63 x}{10} > 0$$
$$\frac{189}{5} - \frac{59 \cdot 63}{10 \cdot 10} > 0$$
the solution of our inequality is:
$$x < 6$$
$$\frac{189}{5} - \frac{63 x}{10} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{189}{5} - \frac{63 x}{10} = 0$$
Solve:
Given the linear equation:
(189/5)-(63/10)*x = 0
Expand brackets in the left part
189/5-63/10x = 0
Move free summands (without x)
from left part to right part, we given:
$$- \frac{63 x}{10} = - \frac{189}{5}$$
Divide both parts of the equation by -63/10
x = -189/5 / (-63/10)
$$x_{1} = 6$$
$$x_{1} = 6$$
This roots
$$x_{1} = 6$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 6$$
=
$$\frac{59}{10}$$
substitute to the expression
$$\frac{189}{5} - \frac{63 x}{10} > 0$$
$$\frac{189}{5} - \frac{59 \cdot 63}{10 \cdot 10} > 0$$
63 --- > 0 100
the solution of our inequality is:
$$x < 6$$
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