Solve :
`(3x-2)/(4)-(2x+3)/(3)=(2)/(3)-x`

Answer

To solve the equation

\[ \frac{3x - 2}{4} - \frac{2x + 3}{3} = \frac{2}{3} - x, \]

we will follow these steps:

### Step 1: Eliminate the fractions by finding a common denominator.
The denominators in the equation are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12. We will multiply each term by 12 to eliminate the fractions.

\[ 12 \left(\frac{3x - 2}{4}\right) - 12 \left(\frac{2x + 3}{3}\right) = 12 \left(\frac{2}{3}\right) - 12x. \]

### Step 2: Simplify each term.
Now we simplify each term:

1. \(12 \left(\frac{3x - 2}{4}\right) = 3(3x - 2) = 9x - 6\),
2. \(12 \left(\frac{2x + 3}{3}\right) = 4(2x + 3) = 8x + 12\),
3. \(12 \left(\frac{2}{3}\right) = 8\).

Putting it all together, we have:

\[ 9x - 6 - (8x + 12) = 8 - 12x. \]

### Step 3: Distribute and combine like terms.
Distributing the negative sign in the left side:

\[ 9x - 6 - 8x - 12 = 8 - 12x. \]

Now combine like terms on the left side:

\[ (9x - 8x) + (-6 - 12) = 8 - 12x, \]

which simplifies to:

\[ x - 18 = 8 - 12x. \]

### Step 4: Move all terms involving \(x\) to one side.
Add \(12x\) to both sides:

\[ x + 12x - 18 = 8. \]

This simplifies to:

\[ 13x - 18 = 8. \]

### Step 5: Move the constant to the other side.
Add 18 to both sides:

\[ 13x = 8 + 18, \]

which simplifies to:

\[ 13x = 26. \]

### Step 6: Solve for \(x\).
Divide both sides by 13:

\[ x = \frac{26}{13} = 2. \]

Thus, the solution to the equation is

\[ \boxed{2}. \]

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