Mister Exam
(x−4)^4>0. inequation
The solution
Detail solution
Given the inequality:
$$\left(x - 4\right)^{4} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(x - 4\right)^{4} = 0$$
Solve:
Given the equation
$$\left(x - 4\right)^{4} = 0$$
so
$$x - 4 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = 4$$
We get the answer: x = 4
$$x_{1} = 4$$
$$x_{1} = 4$$
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
$$\left(x - 4\right)^{4} > 0$$
$$\left(-4 + \frac{39}{10}\right)^{4} > 0$$
the solution of our inequality is:
$$x < 4$$
$$\left(x - 4\right)^{4} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(x - 4\right)^{4} = 0$$
Solve:
Given the equation
$$\left(x - 4\right)^{4} = 0$$
so
$$x - 4 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = 4$$
We get the answer: x = 4
$$x_{1} = 4$$
$$x_{1} = 4$$
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
$$\left(x - 4\right)^{4} > 0$$
$$\left(-4 + \frac{39}{10}\right)^{4} > 0$$
1/10000 > 0
the solution of our inequality is:
$$x < 4$$
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x1
Solving inequality on a graph
Rapid solution
[src]
And(x > -oo, x < oo, x != 4)
$$x > -\infty \wedge x < \infty \wedge x \neq 4$$
(x > -oo)∧(x < oo)∧(Ne(x, 4))
Rapid solution 2
[src]
(-oo, 4) U (4, oo)
$$x\ in\ \left(-\infty, 4\right) \cup \left(4, \infty\right)$$
x in Union(Interval.open(-oo, 4), Interval.open(4, oo))