In the expression
`24 -[2.4 -{0.24 xx 2- (0.024 - x)}] = 22.0589` , the value of x is

Options

A. `0.0024`
B. `0.024`
C. `0.24`
D. `2.4`

Answer

To solve the expression \( 24 - [2.4 - \{0.24 \times 2 - (0.024 - x)\}] = 22.0589 \), we will follow the order of operations (BODMAS/BIDMAS). Here’s a step-by-step breakdown of the solution:

### Step 1: Set up the equation
We start with the equation:
\[ 24 - [2.4 - \{0.24 \times 2 - (0.024 - x)\}] = 22.0589 \]

### Step 2: Simplify the expression inside the brackets
First, we need to simplify the expression inside the brackets:
\[ 0.24 \times 2 = 0.48 \]
So, we can rewrite the equation as:
\[ 24 - [2.4 - \{0.48 - (0.024 - x)\}] = 22.0589 \]

### Step 3: Simplify the expression inside the curly brackets
Next, we simplify the expression inside the curly brackets:
\[ 0.024 - x \text{ becomes } -0.024 + x \]
Thus, we have:
\[ 24 - [2.4 - (0.48 - 0.024 + x)] = 22.0589 \]

### Step 4: Combine the terms inside the brackets
Now, we can rewrite the equation:
\[ 24 - [2.4 - 0.48 + 0.024 - x] = 22.0589 \]
Calculating \(2.4 - 0.48 + 0.024\):
\[ 2.4 - 0.48 = 1.92 \]
\[ 1.92 + 0.024 = 1.944 \]
So the equation simplifies to:
\[ 24 - [1.944 - x] = 22.0589 \]

### Step 5: Distribute the negative sign
Distributing the negative sign gives us:
\[ 24 - 1.944 + x = 22.0589 \]
This simplifies to:
\[ 22.056 + x = 22.0589 \]

### Step 6: Solve for x
Now, we isolate \(x\):
\[ x = 22.0589 - 22.056 \]
Calculating this gives:
\[ x = 0.0029 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{0.0029} \]