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Solving inequalities/ (-x/8)+1/3>0

(-x/8)+1/3>0 inequation

A inequation with variable

The solution

You have entered [src] 
-x    1    
--- + - > 0
 8    3
(−1)x8+13>0\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0 
(-x)/8 + 1/3 > 0
Detail solution
Given the inequality:
(−1)x8+13>0\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0
To solve this inequality, we must first solve the corresponding equation:
(−1)x8+13=0\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:
−x8=−13- \frac{x}{8} = - \frac{1}{3}
Divide both parts of the equation by -1/8
x = -1/3 / (-1/8)

x1=83x_{1} = \frac{8}{3}
x1=83x_{1} = \frac{8}{3}
This roots
x1=83x_{1} = \frac{8}{3}
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x0<x1x_{0} < x_{1}
For example, let's take the point
x0=x1−110x_{0} = x_{1} - \frac{1}{10}
=
−110+83- \frac{1}{10} + \frac{8}{3}
=
7730\frac{77}{30}
substitute to the expression
(−1)x8+13>0\frac{\left(-1\right) x}{8} + \frac{1}{3} > 0
(−1)77308+13>0\frac{\left(-1\right) \frac{77}{30}}{8} + \frac{1}{3} > 0
1/80 > 0

the solution of our inequality is:
x<83x < \frac{8}{3}
 _____          
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       x1
Solving inequality on a graph
02468-4-2102-2
Rapid solution [src] 
And(-oo < x, x < 8/3)
−∞<x∧x<83-\infty < x \wedge x < \frac{8}{3} 
(-oo < x)∧(x < 8/3)
Rapid solution 2 [src] 
(-oo, 8/3)
x in (−∞,83)x\ in\ \left(-\infty, \frac{8}{3}\right) 
x in Interval.open(-oo, 8/3)
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