[tex]\frac{4x-3}{2} - \frac{5-2x}{3} = \frac{3x-4}{3}[/tex]

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вопрос

To solve this equation, we first need to find a common denominator for all fractions involved. In this case, the common denominator is 6.

The equation will become:

[tex]\frac{3(4x-3)}{6} - \frac{2(5-2x)}{6} = \frac{2(3x-4)}{6}[/tex]

Simplify each fraction:

[tex]\frac{12x-9}{6} - \frac{10-4x}{6} = \frac{6x-8}{6}[/tex]

Next, we combine the fractions:

[tex]\frac{12x-9 - 10 + 4x}{6} = \frac{6x-8}{6}[/tex]

Simplify further:

[tex]\frac{16x - 19}{6} = \frac{6x - 8}{6}[/tex]

To remove the fractions, multiply each side by 6:

[tex]16x - 19 = 6x - 8[/tex]

Now, we solve for x:

16x - 19 - 6x = - 8

10x - 19 = -8

10x = 11

x = 11/10

Therefore, the solution to the equation is x = 11/10.