Mister Exam
2x/3-(x+)1/4<=-2 inequation
The solution
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2*x x --- - - <= -2 3 4
$$- \frac{x}{4} + \frac{2 x}{3} \leq -2$$
-x/4 + (2*x)/3 <= -2
Detail solution
Given the inequality:
$$- \frac{x}{4} + \frac{2 x}{3} \leq -2$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{x}{4} + \frac{2 x}{3} = -2$$
Solve:
Given the linear equation:
Expand brackets in the left part
Looking for similar summands in the left part:
Divide both parts of the equation by 5/12
$$x_{1} = - \frac{24}{5}$$
$$x_{1} = - \frac{24}{5}$$
This roots
$$x_{1} = - \frac{24}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{24}{5} + - \frac{1}{10}$$
=
$$- \frac{49}{10}$$
substitute to the expression
$$- \frac{x}{4} + \frac{2 x}{3} \leq -2$$
$$\frac{\left(- \frac{49}{10}\right) 2}{3} - \frac{-49}{4 \cdot 10} \leq -2$$
the solution of our inequality is:
$$x \leq - \frac{24}{5}$$
$$- \frac{x}{4} + \frac{2 x}{3} \leq -2$$
To solve this inequality, we must first solve the corresponding equation:
$$- \frac{x}{4} + \frac{2 x}{3} = -2$$
Solve:
Given the linear equation:
2*x/3-(x)*1/4 = -2
Expand brackets in the left part
2*x/3-x*1/4 = -2
Looking for similar summands in the left part:
5*x/12 = -2
Divide both parts of the equation by 5/12
x = -2 / (5/12)
$$x_{1} = - \frac{24}{5}$$
$$x_{1} = - \frac{24}{5}$$
This roots
$$x_{1} = - \frac{24}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{24}{5} + - \frac{1}{10}$$
=
$$- \frac{49}{10}$$
substitute to the expression
$$- \frac{x}{4} + \frac{2 x}{3} \leq -2$$
$$\frac{\left(- \frac{49}{10}\right) 2}{3} - \frac{-49}{4 \cdot 10} \leq -2$$
-49 ---- <= -2 24
the solution of our inequality is:
$$x \leq - \frac{24}{5}$$
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Solving inequality on a graph
Rapid solution
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And(x <= -24/5, -oo < x)
$$x \leq - \frac{24}{5} \wedge -\infty < x$$
(x <= -24/5)∧(-oo < x)
Rapid solution 2
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(-oo, -24/5]
$$x\ in\ \left(-\infty, - \frac{24}{5}\right]$$
x in Interval(-oo, -24/5)