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13-4*x>21 inequation

A inequation with variable

The solution

You have entered [src]
13 - 4*x > 21
$$13 - 4 x > 21$$
13 - 4*x > 21
Detail solution
Given the inequality:
$$13 - 4 x > 21$$
To solve this inequality, we must first solve the corresponding equation:
$$13 - 4 x = 21$$
Solve:
Given the linear equation:
13-4*x = 21

Move free summands (without x)
from left part to right part, we given:
$$- 4 x = 8$$
Divide both parts of the equation by -4
x = 8 / (-4)

$$x_{1} = -2$$
$$x_{1} = -2$$
This roots
$$x_{1} = -2$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$13 - 4 x > 21$$
$$13 - \frac{\left(-21\right) 4}{10} > 21$$
107/5 > 21

the solution of our inequality is:
$$x < -2$$
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Solving inequality on a graph
Rapid solution 2 [src]
(-oo, -2)
$$x\ in\ \left(-\infty, -2\right)$$
x in Interval.open(-oo, -2)
Rapid solution [src]
And(-oo < x, x < -2)
$$-\infty < x \wedge x < -2$$
(-oo < x)∧(x < -2)