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(x-2)/5-(3x+2)/6=2/3-x

(x-2)/5-(3x+2)/6=2/3-x equation

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Numerical solution:

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The solution

You have entered [src]
x - 2   3*x + 2          
----- - ------- = 2/3 - x
  5        6             
$$\frac{x - 2}{5} - \frac{3 x + 2}{6} = - x + \frac{2}{3}$$
Detail solution
Given the linear equation:
(x-2)/5-(3*x+2)/6 = 2/3-x

Expand brackets in the left part
x/5-2/5-3*x/6-2/6 = 2/3-x

Looking for similar summands in the left part:
-11/15 - 3*x/10 = 2/3-x

Move free summands (without x)
from left part to right part, we given:
$$- \frac{3 x}{10} = - x + \frac{7}{5}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{7 x}{10} = \frac{7}{5}$$
Divide both parts of the equation by 7/10
x = 7/5 / (7/10)

We get the answer: x = 2
The graph
Rapid solution [src]
x1 = 2
$$x_{1} = 2$$
Sum and product of roots [src]
sum
0 + 2
$$0 + 2$$
=
2
$$2$$
product
1*2
$$1 \cdot 2$$
=
2
$$2$$
2
Numerical answer [src]
x1 = 2.0
x1 = 2.0
The graph
(x-2)/5-(3x+2)/6=2/3-x equation