Mister Exam
-63-16x>0 inequation
The solution
Detail solution
Given the inequality:
$$- 16 x - 63 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- 16 x - 63 = 0$$
Solve:
Given the linear equation:
Move free summands (without x)
from left part to right part, we given:
$$- 16 x = 63$$
Divide both parts of the equation by -16
$$x_{1} = - \frac{63}{16}$$
$$x_{1} = - \frac{63}{16}$$
This roots
$$x_{1} = - \frac{63}{16}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{63}{16} + - \frac{1}{10}$$
=
$$- \frac{323}{80}$$
substitute to the expression
$$- 16 x - 63 > 0$$
$$-63 - \frac{\left(-323\right) 16}{80} > 0$$
the solution of our inequality is:
$$x < - \frac{63}{16}$$
$$- 16 x - 63 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$- 16 x - 63 = 0$$
Solve:
Given the linear equation:
-63-16*x = 0
Move free summands (without x)
from left part to right part, we given:
$$- 16 x = 63$$
Divide both parts of the equation by -16
x = 63 / (-16)
$$x_{1} = - \frac{63}{16}$$
$$x_{1} = - \frac{63}{16}$$
This roots
$$x_{1} = - \frac{63}{16}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{63}{16} + - \frac{1}{10}$$
=
$$- \frac{323}{80}$$
substitute to the expression
$$- 16 x - 63 > 0$$
$$-63 - \frac{\left(-323\right) 16}{80} > 0$$
8/5 > 0
the solution of our inequality is:
$$x < - \frac{63}{16}$$
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x1
Solving inequality on a graph
Rapid solution 2
[src]
-63
(-oo, ----)
16
$$x\ in\ \left(-\infty, - \frac{63}{16}\right)$$
x in Interval.open(-oo, -63/16)
Rapid solution
[src]
/ -63 \ And|-oo < x, x < ----| \ 16 /
$$-\infty < x \wedge x < - \frac{63}{16}$$
(-oo < x)∧(x < -63/16)