Mister Exam
x+3.3<=0 inequation
The solution
Detail solution
Given the inequality:
$$x + \frac{33}{10} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x + \frac{33}{10} = 0$$
Solve:
Given the linear equation:
Expand brackets in the left part
Move free summands (without x)
from left part to right part, we given:
$$x = - \frac{33}{10}$$
$$x_{1} = - \frac{33}{10}$$
$$x_{1} = - \frac{33}{10}$$
This roots
$$x_{1} = - \frac{33}{10}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{33}{10} + - \frac{1}{10}$$
=
$$- \frac{17}{5}$$
substitute to the expression
$$x + \frac{33}{10} \leq 0$$
$$- \frac{17}{5} + \frac{33}{10} \leq 0$$
the solution of our inequality is:
$$x \leq - \frac{33}{10}$$
$$x + \frac{33}{10} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x + \frac{33}{10} = 0$$
Solve:
Given the linear equation:
x+(33/10) = 0
Expand brackets in the left part
x+33/10 = 0
Move free summands (without x)
from left part to right part, we given:
$$x = - \frac{33}{10}$$
$$x_{1} = - \frac{33}{10}$$
$$x_{1} = - \frac{33}{10}$$
This roots
$$x_{1} = - \frac{33}{10}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{33}{10} + - \frac{1}{10}$$
=
$$- \frac{17}{5}$$
substitute to the expression
$$x + \frac{33}{10} \leq 0$$
$$- \frac{17}{5} + \frac{33}{10} \leq 0$$
-1/10 <= 0
the solution of our inequality is:
$$x \leq - \frac{33}{10}$$
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x1
Solving inequality on a graph
Rapid solution
[src]
/ -33 \ And|x <= ----, -oo < x| \ 10 /
$$x \leq - \frac{33}{10} \wedge -\infty < x$$
(x <= -33/10)∧(-oo < x)
Rapid solution 2
[src]
-33
(-oo, ----]
10
$$x\ in\ \left(-\infty, - \frac{33}{10}\right]$$
x in Interval(-oo, -33/10)