If `0.001 +1.01 + 1.001 -(1.03xx0.1) + (1.11 div 0.1) + x = 1.4 xx ((1)/(10))^(-1)`, then the value of x is

Options

A. `0.919`
B. `0.785`
C. `0.758`
D. `0.991`

Answer

To solve the equation \(0.001 + 1.01 + 1.001 - (1.03 \times 0.1) + \left(\frac{1.11}{0.1}\right) + x = 1.4 \times 10^{-1}\), we will follow these steps:

### Step 1: Calculate the left-hand side components
1. **Add the first three numbers:**
\[ 0.001 + 1.01 + 1.001 = 2.012 \]

**Hint:** When adding decimal numbers, align the decimal points for easier addition.

2. **Calculate \(1.03 \times 0.1\):**
\[ 1.03 \times 0.1 = 0.103 \]

**Hint:** Multiplying by 0.1 is the same as moving the decimal point one place to the left.

3. **Calculate \(\frac{1.11}{0.1}\):**
\[ \frac{1.11}{0.1} = 11.1 \]

**Hint:** Dividing by 0.1 is equivalent to multiplying by 10.

### Step 2: Substitute the calculated values back into the equation
Now substitute the calculated values into the equation:
\[ 2.012 - 0.103 + 11.1 + x = 1.4 \times 10^{-1} \]

### Step 3: Calculate \(1.4 \times 10^{-1}\)
\[ 1.4 \times 10^{-1} = 0.14 \]

**Hint:** The notation \(10^{-1}\) means to divide by 10.

### Step 4: Simplify the left-hand side
Now, simplify the left-hand side:
\[ 2.012 - 0.103 = 1.909 \]
\[ 1.909 + 11.1 = 13.009 \]

### Step 5: Set up the equation for \(x\)
Now we have:
\[ 13.009 + x = 0.14 \]

### Step 6: Solve for \(x\)
To find \(x\), subtract \(13.009\) from both sides:
\[ x = 0.14 - 13.009 \]
\[ x = -12.869 \]

### Final Answer
The value of \(x\) is:
\[ \boxed{-12.869} \]