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(1/2)*x>=4 inequation

A inequation with variable

The solution

You have entered [src]
x     
- >= 4
2     
$$\frac{x}{2} \geq 4$$
x/2 >= 4
Detail solution
Given the inequality:
$$\frac{x}{2} \geq 4$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{x}{2} = 4$$
Solve:
Given the linear equation:
(1/2)*x = 4

Expand brackets in the left part
1/2x = 4

Divide both parts of the equation by 1/2
x = 4 / (1/2)

$$x_{1} = 8$$
$$x_{1} = 8$$
This roots
$$x_{1} = 8$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 8$$
=
$$\frac{79}{10}$$
substitute to the expression
$$\frac{x}{2} \geq 4$$
$$\frac{79}{2 \cdot 10} \geq 4$$
79     
-- >= 4
20     

but
79    
-- < 4
20    

Then
$$x \leq 8$$
no execute
the solution of our inequality is:
$$x \geq 8$$
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       x1
Solving inequality on a graph
Rapid solution 2 [src]
[8, oo)
$$x\ in\ \left[8, \infty\right)$$
x in Interval(8, oo)
Rapid solution [src]
And(8 <= x, x < oo)
$$8 \leq x \wedge x < \infty$$
(8 <= x)∧(x < oo)