Solve :
`(3x-2)/(3)+(2x+3)/(2)=x+(7)/(6)`

Answer

To solve the equation

\[ \frac{3x-2}{3} + \frac{2x+3}{2} = x + \frac{7}{6} \]

we will follow these steps:

### Step 1: Write the equation
We start with the given equation:

\[ \frac{3x-2}{3} + \frac{2x+3}{2} = x + \frac{7}{6} \]

### Step 2: Find the LCM of the denominators
The denominators in the equation are 3, 2, and 6. The least common multiple (LCM) of these numbers is 6.

### Step 3: Rewrite each term with the LCM
Now, we will rewrite each fraction with a denominator of 6:

- For \(\frac{3x-2}{3}\), we multiply the numerator and denominator by 2:
\[ \frac{2(3x-2)}{6} = \frac{6x - 4}{6} \]

- For \(\frac{2x+3}{2}\), we multiply the numerator and denominator by 3:
\[ \frac{3(2x+3)}{6} = \frac{6x + 9}{6} \]

- The term \(x + \frac{7}{6}\) can be rewritten as:
\[ \frac{6x}{6} + \frac{7}{6} = \frac{6x + 7}{6} \]

### Step 4: Combine the left-hand side
Now we can combine the left-hand side:
\[ \frac{6x - 4 + 6x + 9}{6} = \frac{12x + 5}{6} \]

### Step 5: Set the equation
Now we have:
\[ \frac{12x + 5}{6} = \frac{6x + 7}{6} \]

### Step 6: Eliminate the denominators
Since both sides have the same denominator, we can eliminate it:
\[ 12x + 5 = 6x + 7 \]

### Step 7: Move all x terms to one side
Subtract \(6x\) from both sides:
\[ 12x - 6x + 5 = 7 \]
This simplifies to:
\[ 6x + 5 = 7 \]

### Step 8: Move constant terms to the other side
Subtract 5 from both sides:
\[ 6x = 7 - 5 \]
This simplifies to:
\[ 6x = 2 \]

### Step 9: Solve for x
Now, divide both sides by 6:
\[ x = \frac{2}{6} = \frac{1}{3} \]

### Final Answer
Thus, the solution to the equation is:
\[ x = \frac{1}{3} \]

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