If `(1//4 of x) - (4//5 f 6//7)` equal `-9//7` then values of x is

Options

A. `-12`
B. `-2.4`
C. `-3.6`
D. `-14`

Answer

To solve the equation \( \frac{1}{4}x - \frac{4}{5} \cdot \frac{6}{7} = -\frac{9}{7} \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{1}{4}x - \frac{4}{5} \cdot \frac{6}{7} = -\frac{9}{7} \]

### Step 2: Simplify the second term
Calculate \( \frac{4}{5} \cdot \frac{6}{7} \):
\[ \frac{4 \cdot 6}{5 \cdot 7} = \frac{24}{35} \]
Now, substitute this back into the equation:
\[ \frac{1}{4}x - \frac{24}{35} = -\frac{9}{7} \]

### Step 3: Move the fraction to the other side
Add \( \frac{24}{35} \) to both sides:
\[ \frac{1}{4}x = -\frac{9}{7} + \frac{24}{35} \]

### Step 4: Find a common denominator
The common denominator for \( 7 \) and \( 35 \) is \( 35 \). Convert \( -\frac{9}{7} \) to have a denominator of \( 35 \):
\[ -\frac{9}{7} = -\frac{9 \cdot 5}{7 \cdot 5} = -\frac{45}{35} \]
Now substitute this back into the equation:
\[ \frac{1}{4}x = -\frac{45}{35} + \frac{24}{35} \]

### Step 5: Combine the fractions
Now combine the fractions on the right:
\[ \frac{1}{4}x = \frac{-45 + 24}{35} = \frac{-21}{35} \]

### Step 6: Solve for x
To isolate \( x \), multiply both sides by \( 4 \):
\[ x = 4 \cdot \frac{-21}{35} \]
This simplifies to:
\[ x = \frac{-84}{35} \]

### Step 7: Simplify the fraction
Now simplify \( \frac{-84}{35} \):
\[ x = -\frac{84 \div 7}{35 \div 7} = -\frac{12}{5} \]
This can also be expressed as:
\[ x = -2.4 \]

### Final Answer:
Thus, the value of \( x \) is:
\[ \boxed{-2.4} \]