Simplify the given expression and find its value at `x= -44 : 2(x - 4) - (x + 4) + 54 + (x - 5) - (x - 10)`.

Options

A. 4
B. 8
C. `-8`
D. 3

Answer

To simplify the expression \( 2(x - 4) - (x + 4) + 54 + (x - 5) - (x - 10) \) and find its value at \( x = -44 \), we can follow these steps:

### Step 1: Distribute the terms
First, we distribute the \( 2 \) in the first term and the negative signs in the other terms:
\[ 2(x - 4) = 2x - 8 \]
\[ -(x + 4) = -x - 4 \]
\[ +(x - 5) = x - 5 \]
\[ -(x - 10) = -x + 10 \]

Now, we can rewrite the expression:
\[ 2x - 8 - x - 4 + 54 + x - 5 - x + 10 \]

### Step 2: Combine like terms
Next, we combine all the like terms:
- Combine the \( x \) terms:
\[ 2x - x + x - x = (2 - 1 + 1 - 1)x = x \]

- Combine the constant terms:
\[ -8 - 4 + 54 - 5 + 10 = (-8 - 4 - 5) + (54 + 10) = -17 + 64 = 47 \]

So, the expression simplifies to:
\[ x + 47 \]

### Step 3: Substitute \( x = -44 \)
Now, we substitute \( x = -44 \) into the simplified expression:
\[ -44 + 47 = 3 \]

### Final Answer
Thus, the value of the expression at \( x = -44 \) is:
\[ \boxed{3} \]