Question

(2х+1)/3+2=(3х-2)/2+(х+1)/3

Answer 1

$\frac{2x + 1}{3} + 2 = \frac{3x - 2}{2} + \frac{x + 1}{3}$

Домножим обе части на 6

$2(2x + 1) + 6 \times 2 = 3(3x - 2) + 2(x + 1) \\ \\ 4x + 2 + 12 = 9x - 6 + 2x + 2 \\ \\ 4x + 14 = 11x - 4 \\ \\ 11x - 4x = 14 + 4 \\ \\ 7x = 18 \\ \\ x = \frac{18}{7} = 2 \frac{4}{7}$

Answer 2

To solve the equation:

(2x+1)/3 + 2 = (3x-2)/2 + (x+1)/3

First, we'll need to get rid of the denominators. We can do this by finding a common denominator for both sides of the equation. The least common multiple of 2 and 3 is 6, so we'll use that as our common denominator.

Multiplying both sides by 6, we get:

2(2x+1) + 18 = 3(3x-2) + 2(x+1)

Expanding the brackets, we get:

4x + 2 + 18 = 9x - 6 + 2x + 2

Simplifying, we get:

4x + 20 = 11x - 4

Bringing all the x terms to one side and all the constants to the other side, we get:

4x - 11x = -4 - 20

Simplifying further, we get:

-7x = -24

Finally, dividing both sides by -7, we get:

x = 24/7

Therefore, the solution to the equation is x = 24/7.