Find the value of X `-2(1)/(9)-6 `= X

Options

A. `-8(1)/(9)`
B. `8(1)/(9)`
C. (4(1)/(9)`
D. `-4(1)/(9)`

Answer

To solve the equation \(-2\frac{1}{9} - 6 = X\), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \(-2\frac{1}{9}\) can be converted to an improper fraction.

To do this, multiply the whole number part by the denominator and add the numerator:
\[ -2\frac{1}{9} = -\left(2 \times 9 + 1\right) / 9 = -\left(18 + 1\right) / 9 = -\frac{19}{9} \]

### Step 2: Rewrite the equation
Now we can rewrite the equation with the improper fraction:
\[ -\frac{19}{9} - 6 = X \]

### Step 3: Convert the whole number to a fraction
Next, we need to express \(-6\) as a fraction with the same denominator (9):
\[ -6 = -\frac{6 \times 9}{9} = -\frac{54}{9} \]

### Step 4: Combine the fractions
Now we can combine the two fractions:
\[ -\frac{19}{9} - \frac{54}{9} = X \]
\[ X = -\frac{19 + 54}{9} = -\frac{73}{9} \]

### Step 5: Final answer
Thus, the value of \(X\) is:
\[ X = -\frac{73}{9} \]

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