यदि `A= -(2x+3) , B= -3(x-2)` तथा `C=-2x+7` है। तब K का मान ज्ञात करो, यदि `(A+B+C)=Kx`

Options

A. 3
B. `-7`
C. 6
D. `-5`

Answer

To find the value of \( K \) given the equations \( A = -(2x + 3) \), \( B = -3(x - 2) \), and \( C = -2x + 7 \), we will follow these steps:

### Step 1: Substitute the values of A, B, and C
We start by substituting the expressions for \( A \), \( B \), and \( C \):
\[ A + B + C = -(2x + 3) + -3(x - 2) + (-2x + 7) \]

### Step 2: Simplify each term
Now, let's simplify each term:
- For \( A \):
\[ A = -2x - 3 \]
- For \( B \):
\[ B = -3(x - 2) = -3x + 6 \]
- For \( C \):
\[ C = -2x + 7 \]

### Step 3: Combine the expressions
Now, we can combine all the simplified expressions:
\[ A + B + C = (-2x - 3) + (-3x + 6) + (-2x + 7) \]

### Step 4: Combine like terms
Now, we will combine the like terms:
- Combine the \( x \) terms:
\[ -2x - 3x - 2x = -7x \]
- Combine the constant terms:
\[ -3 + 6 + 7 = 10 \]

So, we have:
\[ A + B + C = -7x + 10 \]

### Step 5: Set the equation equal to Kx
We know that \( A + B + C = Kx \). Therefore, we can write:
\[ -7x + 10 = Kx \]

### Step 6: Isolate K
To find \( K \), we need to isolate it. We can rearrange the equation:
\[ Kx = -7x + 10 \]

### Step 7: Equate coefficients
Since we want to express everything in terms of \( K \), we can equate the coefficients of \( x \):
\[ K = -7 \]

### Final Answer
Thus, the value of \( K \) is:
\[ \boxed{-7} \]