If `(-5 x )/(3) + 2 =x-6` then find the value of 'x'.

Options

A. 1
B. 2
C. 3
D. 4

Answer

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

### Step 1: Write the equation
Start with the given equation:
\[ \frac{-5x}{3} + 2 = x - 6 \]

### Step 2: Eliminate the fraction
To eliminate the fraction, we can multiply every term in the equation by 3 (the denominator):
\[ 3 \left(\frac{-5x}{3}\right) + 3(2) = 3(x - 6) \]
This simplifies to:
\[ -5x + 6 = 3x - 18 \]

### Step 3: Rearrange the equation
Next, we will move all terms involving \(x\) to one side and constant terms to the other side. We can add \(5x\) to both sides:
\[ 6 = 3x + 5x - 18 \]
This simplifies to:
\[ 6 = 8x - 18 \]

### Step 4: Isolate \(x\)
Now, we will add 18 to both sides to isolate the term with \(x\):
\[ 6 + 18 = 8x \]
This simplifies to:
\[ 24 = 8x \]

### Step 5: Solve for \(x\)
Finally, divide both sides by 8 to solve for \(x\):
\[ x = \frac{24}{8} \]
This simplifies to:
\[ x = 3 \]

### Conclusion
The value of \(x\) is:
\[ \boxed{3} \]

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