Mister Exam
5x-2(2x-8)<5 inequation
The solution
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5*x - 2*(2*x - 8) < 5
$$5 x - 2 \left(2 x - 8\right) < 5$$
5*x - 2*(2*x - 8) < 5
Detail solution
Given the inequality:
$$5 x - 2 \left(2 x - 8\right) < 5$$
To solve this inequality, we must first solve the corresponding equation:
$$5 x - 2 \left(2 x - 8\right) = 5$$
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:
$$x = -11$$
$$x_{1} = -11$$
$$x_{1} = -11$$
This roots
$$x_{1} = -11$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-11 + - \frac{1}{10}$$
=
$$- \frac{111}{10}$$
substitute to the expression
$$5 x - 2 \left(2 x - 8\right) < 5$$
$$\frac{\left(-111\right) 5}{10} - 2 \left(\frac{\left(-111\right) 2}{10} - 8\right) < 5$$
the solution of our inequality is:
$$x < -11$$
$$5 x - 2 \left(2 x - 8\right) < 5$$
To solve this inequality, we must first solve the corresponding equation:
$$5 x - 2 \left(2 x - 8\right) = 5$$
Solve:
Given the linear equation:
5*x-2*(2*x-8) = 5
Expand brackets in the left part
5*x-2*2*x+2*8 = 5
Looking for similar summands in the left part:
16 + x = 5
Move free summands (without x)
from left part to right part, we given:
$$x = -11$$
$$x_{1} = -11$$
$$x_{1} = -11$$
This roots
$$x_{1} = -11$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-11 + - \frac{1}{10}$$
=
$$- \frac{111}{10}$$
substitute to the expression
$$5 x - 2 \left(2 x - 8\right) < 5$$
$$\frac{\left(-111\right) 5}{10} - 2 \left(\frac{\left(-111\right) 2}{10} - 8\right) < 5$$
49 -- < 5 10
the solution of our inequality is:
$$x < -11$$
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