Mister Exam
2x+4(2x-3)-12x-11 inequation
The solution
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2*x + 4*(2*x - 3) - 12*x - 11 > 0
$$\left(- 12 x + \left(2 x + 4 \left(2 x - 3\right)\right)\right) - 11 > 0$$
-12*x + 2*x + 4*(2*x - 3) - 11 > 0
Detail solution
Given the inequality:
$$\left(- 12 x + \left(2 x + 4 \left(2 x - 3\right)\right)\right) - 11 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- 12 x + \left(2 x + 4 \left(2 x - 3\right)\right)\right) - 11 = 0$$
Solve:
Given the linear equation:
Expand brackets in the left part
Looking for similar summands in the left part:
Move free summands (without x)
from left part to right part, we given:
$$- 2 x = 23$$
Divide both parts of the equation by -2
$$x_{1} = - \frac{23}{2}$$
$$x_{1} = - \frac{23}{2}$$
This roots
$$x_{1} = - \frac{23}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{23}{2} + - \frac{1}{10}$$
=
$$- \frac{58}{5}$$
substitute to the expression
$$\left(- 12 x + \left(2 x + 4 \left(2 x - 3\right)\right)\right) - 11 > 0$$
$$-11 + \left(\left(4 \left(\frac{\left(-58\right) 2}{5} - 3\right) + \frac{\left(-58\right) 2}{5}\right) - \frac{\left(-58\right) 12}{5}\right) > 0$$
the solution of our inequality is:
$$x < - \frac{23}{2}$$
$$\left(- 12 x + \left(2 x + 4 \left(2 x - 3\right)\right)\right) - 11 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(- 12 x + \left(2 x + 4 \left(2 x - 3\right)\right)\right) - 11 = 0$$
Solve:
Given the linear equation:
2*x+4*(2*x-3)-12*x-11 = 0
Expand brackets in the left part
2*x+4*2*x-4*3-12*x-11 = 0
Looking for similar summands in the left part:
-23 - 2*x = 0
Move free summands (without x)
from left part to right part, we given:
$$- 2 x = 23$$
Divide both parts of the equation by -2
x = 23 / (-2)
$$x_{1} = - \frac{23}{2}$$
$$x_{1} = - \frac{23}{2}$$
This roots
$$x_{1} = - \frac{23}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{23}{2} + - \frac{1}{10}$$
=
$$- \frac{58}{5}$$
substitute to the expression
$$\left(- 12 x + \left(2 x + 4 \left(2 x - 3\right)\right)\right) - 11 > 0$$
$$-11 + \left(\left(4 \left(\frac{\left(-58\right) 2}{5} - 3\right) + \frac{\left(-58\right) 2}{5}\right) - \frac{\left(-58\right) 12}{5}\right) > 0$$
1/5 > 0
the solution of our inequality is:
$$x < - \frac{23}{2}$$
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Solving inequality on a graph
Rapid solution 2
[src]
(-oo, -23/2)
$$x\ in\ \left(-\infty, - \frac{23}{2}\right)$$
x in Interval.open(-oo, -23/2)
Rapid solution
[src]
And(-oo < x, x < -23/2)
$$-\infty < x \wedge x < - \frac{23}{2}$$
(-oo < x)∧(x < -23/2)