Mister Exam
(-x/8)+1/3>0 inequation
The solution
You have entered
[src]
-x 1 --- + - > 0 8 3
$$\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0$$
(-x)/8 + 1/3 > 0
Detail solution
Given the inequality:
$$\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(-1\right) x}{8} + \frac{1}{3} = 0$$
Solve:
Given the linear equation:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$- \frac{x}{8} = - \frac{1}{3}$$
Divide both parts of the equation by -1/8
$$x_{1} = \frac{8}{3}$$
$$x_{1} = \frac{8}{3}$$
This roots
$$x_{1} = \frac{8}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{8}{3}$$
=
$$\frac{77}{30}$$
substitute to the expression
$$\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0$$
$$\frac{\left(-1\right) \frac{77}{30}}{8} + \frac{1}{3} > 0$$
the solution of our inequality is:
$$x < \frac{8}{3}$$
$$\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\left(-1\right) x}{8} + \frac{1}{3} = 0$$
Solve:
Given the linear equation:
(-x/8)+1/3 = 0
Expand brackets in the left part
-x/8+1/3 = 0
Move free summands (without x)
from left part to right part, we given:
$$- \frac{x}{8} = - \frac{1}{3}$$
Divide both parts of the equation by -1/8
x = -1/3 / (-1/8)
$$x_{1} = \frac{8}{3}$$
$$x_{1} = \frac{8}{3}$$
This roots
$$x_{1} = \frac{8}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{8}{3}$$
=
$$\frac{77}{30}$$
substitute to the expression
$$\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0$$
$$\frac{\left(-1\right) \frac{77}{30}}{8} + \frac{1}{3} > 0$$
1/80 > 0
the solution of our inequality is:
$$x < \frac{8}{3}$$
_____
\
-------ο-------
x1
Solving inequality on a graph
Rapid solution
[src]
And(-oo < x, x < 8/3)
$$-\infty < x \wedge x < \frac{8}{3}$$
(-oo < x)∧(x < 8/3)
Rapid solution 2
[src]
(-oo, 8/3)
$$x\ in\ \left(-\infty, \frac{8}{3}\right)$$
x in Interval.open(-oo, 8/3)