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Solving inequalities/ 7x<-3

7x<-3 inequation

A inequation with variable

The solution

You have entered [src] 
7*x < -3
7x<−37 x < -3 
7*x < -3
Detail solution
Given the inequality:
7x<−37 x < -3
To solve this inequality, we must first solve the corresponding equation:
7x=−37 x = -3
Solve:
Given the linear equation:
7*x = -3

Divide both parts of the equation by 7
x = -3 / (7)

x1=−37x_{1} = - \frac{3}{7}
x1=−37x_{1} = - \frac{3}{7}
This roots
x1=−37x_{1} = - \frac{3}{7}
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}
=
−37+−110- \frac{3}{7} + - \frac{1}{10}
=
−3770- \frac{37}{70}
substitute to the expression
7x<−37 x < -3
(−37)770<−3\frac{\left(-37\right) 7}{70} < -3
-37      
---- < -3
 10

the solution of our inequality is:
x<−37x < - \frac{3}{7}
 _____          
      \    
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       x1
Solving inequality on a graph
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.0-2020
Rapid solution [src] 
And(-oo < x, x < -3/7)
−∞<x∧x<−37-\infty < x \wedge x < - \frac{3}{7} 
(-oo < x)∧(x < -3/7)
Rapid solution 2 [src] 
(-oo, -3/7)
x in (−∞,−37)x\ in\ \left(-\infty, - \frac{3}{7}\right) 
x in Interval.open(-oo, -3/7)
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