If `(9x - 5)/(7) + ( 6- 3x )/( 2 ) = 3,` then x = _____.

Options

A. `2//3`
B. `3//4`
C. `5//4`
D. `4//3`

Answer

To solve the equation \(\frac{9x - 5}{7} + \frac{6 - 3x}{2} = 3\), we will follow these steps:

### Step 1: Write the equation
We start with the equation:
\[ \frac{9x - 5}{7} + \frac{6 - 3x}{2} = 3 \]

**Hint:** Always start by clearly writing down the equation you need to solve.

### Step 2: Find the Least Common Multiple (LCM)
The denominators are 7 and 2. The LCM of 7 and 2 is 14.

**Hint:** Finding the LCM helps in eliminating the fractions in the equation.

### Step 3: Multiply the entire equation by the LCM
Multiply each term by 14 to eliminate the fractions:
\[ 14 \cdot \frac{9x - 5}{7} + 14 \cdot \frac{6 - 3x}{2} = 14 \cdot 3 \]

This simplifies to:
\[ 2(9x - 5) + 7(6 - 3x) = 42 \]

**Hint:** When multiplying by the LCM, distribute it to each term in the equation.

### Step 4: Distribute the multiplication
Distributing gives us:
\[ 18x - 10 + 42 - 21x = 42 \]

**Hint:** Distributing helps to simplify the equation further.

### Step 5: Combine like terms
Now, combine the terms involving \(x\) and the constant terms:
\[ (18x - 21x) + (-10 + 42) = 42 \]
This simplifies to:
\[ -3x + 32 = 42 \]

**Hint:** Combining like terms makes the equation simpler to solve.

### Step 6: Isolate the variable
Next, isolate the term with \(x\):
\[ -3x = 42 - 32 \]
This simplifies to:
\[ -3x = 10 \]

**Hint:** To isolate \(x\), move constant terms to the other side of the equation.

### Step 7: Solve for \(x\)
Now, divide both sides by -3:
\[ x = \frac{10}{-3} \]
This simplifies to:
\[ x = -\frac{10}{3} \]

**Hint:** When dividing, remember to keep track of the signs.

### Final Answer
Thus, the value of \(x\) is:
\[ x = -\frac{10}{3} \]