Mister Exam
(2x/3)-((x+1)/4)≤2 inequation
The solution
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2*x x + 1 --- - ----- <= 2 3 4
$$\frac{2 x}{3} - \frac{x + 1}{4} \leq 2$$
(2*x)/3 - (x + 1)/4 <= 2
Detail solution
Given the inequality:
$$\frac{2 x}{3} - \frac{x + 1}{4} \leq 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x}{3} - \frac{x + 1}{4} = 2$$
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:
$$\frac{5 x}{12} = \frac{9}{4}$$
Divide both parts of the equation by 5/12
$$x_{1} = \frac{27}{5}$$
$$x_{1} = \frac{27}{5}$$
This roots
$$x_{1} = \frac{27}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{27}{5}$$
=
$$\frac{53}{10}$$
substitute to the expression
$$\frac{2 x}{3} - \frac{x + 1}{4} \leq 2$$
$$- \frac{1 + \frac{53}{10}}{4} + \frac{2 \frac{53}{10}}{3} \leq 2$$
the solution of our inequality is:
$$x \leq \frac{27}{5}$$
$$\frac{2 x}{3} - \frac{x + 1}{4} \leq 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{2 x}{3} - \frac{x + 1}{4} = 2$$
Solve:
Given the linear equation:
(2*x/3)-((x+1)/4) = 2
Expand brackets in the left part
2*x/3-x/4-1/4) = 2
Looking for similar summands in the left part:
-1/4 + 5*x/12 = 2
Move free summands (without x)
from left part to right part, we given:
$$\frac{5 x}{12} = \frac{9}{4}$$
Divide both parts of the equation by 5/12
x = 9/4 / (5/12)
$$x_{1} = \frac{27}{5}$$
$$x_{1} = \frac{27}{5}$$
This roots
$$x_{1} = \frac{27}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{27}{5}$$
=
$$\frac{53}{10}$$
substitute to the expression
$$\frac{2 x}{3} - \frac{x + 1}{4} \leq 2$$
$$- \frac{1 + \frac{53}{10}}{4} + \frac{2 \frac{53}{10}}{3} \leq 2$$
47 -- <= 2 24
the solution of our inequality is:
$$x \leq \frac{27}{5}$$
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Solving inequality on a graph
Rapid solution 2
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(-oo, 27/5]
$$x\ in\ \left(-\infty, \frac{27}{5}\right]$$
x in Interval(-oo, 27/5)
Rapid solution
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And(x <= 27/5, -oo < x)
$$x \leq \frac{27}{5} \wedge -\infty < x$$
(x <= 27/5)∧(-oo < x)