Mister Exam

+x+12>5 inequation

A inequation with variable

The solution

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x + 12 > 5
x+12>5x + 12 > 5
x + 12 > 5
Detail solution
Given the inequality:
x+12>5x + 12 > 5
To solve this inequality, we must first solve the corresponding equation:
x+12=5x + 12 = 5
Solve:
Given the linear equation:
+x+12 = 5

Move free summands (without x)
from left part to right part, we given:
x=7x = -7
x1=7x_{1} = -7
x1=7x_{1} = -7
This roots
x1=7x_{1} = -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=x1110x_{0} = x_{1} - \frac{1}{10}
=
7+110-7 + - \frac{1}{10}
=
7110- \frac{71}{10}
substitute to the expression
x+12>5x + 12 > 5
7110+12>5- \frac{71}{10} + 12 > 5
49    
-- > 5
10    

Then
x<7x < -7
no execute
the solution of our inequality is:
x>7x > -7
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       x1
Solving inequality on a graph
05-25-20-15-10-510-5050
Rapid solution [src]
And(-7 < x, x < oo)
7<xx<-7 < x \wedge x < \infty
(-7 < x)∧(x < oo)
Rapid solution 2 [src]
(-7, oo)
x in (7,)x\ in\ \left(-7, \infty\right)
x in Interval.open(-7, oo)