If `(2x + 3)/(6) + ((2x -3)/(3))= 3,` then the value of x is ____.

Options

A. 7/2
B. 3
C. 1
D. `-2`

Answer

To solve the equation \(\frac{2x + 3}{6} + \frac{2x - 3}{3} = 3\), we will follow these steps:

### Step 1: Make the denominators the same
The denominators in the equation are 6 and 3. The least common multiple (LCM) of 6 and 3 is 6. We can rewrite the second fraction to have a denominator of 6:

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

### Step 2: Combine the fractions
Now that both fractions have the same denominator, we can combine them:

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

### Step 3: Simplify the numerator
Now, simplify the numerator:

\[ 2x + 3 + 4x - 6 = 6x - 3 \]

So, the equation becomes:

\[ \frac{6x - 3}{6} = 3 \]

### Step 4: Cross-multiply
To eliminate the fraction, we can cross-multiply:

\[ 6x - 3 = 3 \times 6 \]

### Step 5: Calculate the right side
Calculate the right side:

\[ 6x - 3 = 18 \]

### Step 6: Solve for \(x\)
Now, add 3 to both sides:

\[ 6x = 18 + 3 \]
\[ 6x = 21 \]

Now, divide both sides by 6:

\[ x = \frac{21}{6} \]

### Step 7: Simplify the fraction
Simplifying \(\frac{21}{6}\):

\[ x = \frac{7}{2} \]

Thus, the value of \(x\) is \(\frac{7}{2}\).

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