Mister Exam
(2x-8)÷(x+30)>0 inequation
The solution
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2*x - 8 ------- > 0 x + 30
$$\frac{2 x - 8}{x + 30} > 0$$
(2*x - 8)/(x + 30) > 0
Detail solution
Given the inequality:
$$\frac{2 x - 8}{x + 30} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x - 8}{x + 30} = 0$$
Solve:
Given the equation:
$$\frac{2 x - 8}{x + 30} = 0$$
Multiply the equation sides by the denominator 30 + x
we get:
$$2 x - 8 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$2 x = 8$$
Divide both parts of the equation by 2
$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$\frac{2 x - 8}{x + 30} > 0$$
$$\frac{-8 + \frac{2 \cdot 39}{10}}{\frac{39}{10} + 30} > 0$$
Then
$$x < 4$$
no execute
the solution of our inequality is:
$$x > 4$$
$$\frac{2 x - 8}{x + 30} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x - 8}{x + 30} = 0$$
Solve:
Given the equation:
$$\frac{2 x - 8}{x + 30} = 0$$
Multiply the equation sides by the denominator 30 + x
we get:
$$2 x - 8 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$2 x = 8$$
Divide both parts of the equation by 2
x = 8 / (2)
$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$\frac{2 x - 8}{x + 30} > 0$$
$$\frac{-8 + \frac{2 \cdot 39}{10}}{\frac{39}{10} + 30} > 0$$
-2/339 > 0
Then
$$x < 4$$
no execute
the solution of our inequality is:
$$x > 4$$
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Solving inequality on a graph
Rapid solution 2
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(-oo, -30) U (4, oo)
$$x\ in\ \left(-\infty, -30\right) \cup \left(4, \infty\right)$$
x in Union(Interval.open(-oo, -30), Interval.open(4, oo))
Rapid solution
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Or(And(-oo < x, x < -30), And(4 < x, x < oo))
$$\left(-\infty < x \wedge x < -30\right) \vee \left(4 < x \wedge x < \infty\right)$$
((-oo < x)∧(x < -30))∨((4 < x)∧(x < oo))