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Solving inequalities/ 3-2x<5

3-2x<5 inequation

A inequation with variable

The solution

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3 - 2*x < 5
3−2x<53 - 2 x < 5 
3 - 2*x < 5
Detail solution
Given the inequality:
3−2x<53 - 2 x < 5
To solve this inequality, we must first solve the corresponding equation:
3−2x=53 - 2 x = 5
Solve:
Given the linear equation:
3-2*x = 5

Move free summands (without x)
from left part to right part, we given:
−2x=2- 2 x = 2
Divide both parts of the equation by -2
x = 2 / (-2)

x1=−1x_{1} = -1
x1=−1x_{1} = -1
This roots
x1=−1x_{1} = -1
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}
=
−1+−110-1 + - \frac{1}{10}
=
−1110- \frac{11}{10}
substitute to the expression
3−2x<53 - 2 x < 5
3−(−11)210<53 - \frac{\left(-11\right) 2}{10} < 5
26/5 < 5

but
26/5 > 5

Then
x<−1x < -1
no execute
the solution of our inequality is:
x>−1x > -1
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       x1
Solving inequality on a graph
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.020-10
Rapid solution [src] 
And(-1 < x, x < oo)
−1<x∧x<∞-1 < x \wedge x < \infty 
(-1 < x)∧(x < oo)
Rapid solution 2 [src] 
(-1, oo)
x in (−1,∞)x\ in\ \left(-1, \infty\right) 
x in Interval.open(-1, oo)
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