Solve : `(5x-3)/(2)- (3x-2)/(3)=(2)/(3)`

Options

A. `x=2`
B. `x=1`
C. `x=3`
D. `x=4`

Answer

To solve the equation \(\frac{5x-3}{2} - \frac{3x-2}{3} = \frac{2}{3}\), we will follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 2 and 3. The least common multiple (LCM) of 2 and 3 is 6. We will multiply each term by 6 to eliminate the denominators.

\[ 6 \left(\frac{5x-3}{2}\right) - 6 \left(\frac{3x-2}{3}\right) = 6 \left(\frac{2}{3}\right) \]

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

- For the first term:
\[ 6 \cdot \frac{5x-3}{2} = 3(5x - 3) = 15x - 9 \]

- For the second term:
\[ 6 \cdot \frac{3x-2}{3} = 2(3x - 2) = 6x - 4 \]

- For the right side:
\[ 6 \cdot \frac{2}{3} = 4 \]

Putting it all together, we have:
\[ 15x - 9 - (6x - 4) = 4 \]

### Step 3: Distribute and combine like terms
Distributing the negative sign in the equation:
\[ 15x - 9 - 6x + 4 = 4 \]

Now combine like terms:
\[ (15x - 6x) + (-9 + 4) = 4 \]
\[ 9x - 5 = 4 \]

### Step 4: Isolate the variable
Now, we will isolate \(x\) by adding 5 to both sides:
\[ 9x - 5 + 5 = 4 + 5 \]
\[ 9x = 9 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 9:
\[ x = \frac{9}{9} = 1 \]

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

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