Solve :
`(6x+1)/(2)+1=(7x-3)/(3)`

Answer

To solve the equation

\[ \frac{6x + 1}{2} + 1 = \frac{7x - 3}{3}, \]

we will follow these steps:

### Step 1: Simplify the equation
First, we can rewrite the left side of the equation. The term \(1\) can be expressed as \(\frac{2}{2}\) to have a common denominator with \(\frac{6x + 1}{2}\):

\[ \frac{6x + 1}{2} + \frac{2}{2} = \frac{7x - 3}{3}. \]

### Step 2: Combine the fractions on the left side
Now, we combine the fractions on the left side:

\[ \frac{6x + 1 + 2}{2} = \frac{7x - 3}{3}. \]

This simplifies to:

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

### Step 3: Cross-multiply
Next, we will cross-multiply to eliminate the fractions:

\[ 3(6x + 3) = 2(7x - 3). \]

### Step 4: Distribute
Now, we distribute on both sides:

\[ 18x + 9 = 14x - 6. \]

### Step 5: Move variables to one side
Next, we will move all terms involving \(x\) to one side and the constant terms to the other side. Subtract \(14x\) from both sides:

\[ 18x - 14x + 9 = -6. \]

This simplifies to:

\[ 4x + 9 = -6. \]

### Step 6: Move constants to the other side
Now, subtract \(9\) from both sides:

\[ 4x = -6 - 9. \]

This simplifies to:

\[ 4x = -15. \]

### Step 7: Solve for \(x\)
Finally, divide both sides by \(4\):

\[ x = \frac{-15}{4}. \]

### Final Answer
Thus, the solution to the equation is

\[ x = -\frac{15}{4}. \]

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