If `x [-2 {-4(-a)}] + 5[-2{-2(-a)}] = 4a`, then x =

Options

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

Answer

To solve the equation \( x[-2{-4(-a)}] + 5[-2{-2(-a)}] = 4a \), we will follow these steps:

### Step 1: Simplify the expressions inside the brackets
First, we simplify the expressions inside the brackets.

1. For the first term:
\[ -4(-a) = 4a \]
So,
\[ -2{-4(-a)} = -2(4a) = -8a \]

2. For the second term:
\[ -2(-a) = 2a \]
So,
\[ -2{-2(-a)} = -2(2a) = -4a \]

### Step 2: Substitute back into the equation
Now substitute these simplified expressions back into the original equation:
\[ x[-8a] + 5[-4a] = 4a \]

### Step 3: Distribute and combine like terms
Distributing the terms gives us:
\[ -8ax - 20a = 4a \]

### Step 4: Move all terms involving \( a \) to one side
Now, we will move \( -20a \) to the right side of the equation:
\[ -8ax = 4a + 20a \]
This simplifies to:
\[ -8ax = 24a \]

### Step 5: Solve for \( x \)
Now, divide both sides by \( -8a \) (assuming \( a \neq 0 \)):
\[ x = \frac{24a}{-8a} \]
This simplifies to:
\[ x = -3 \]

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

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