If 1/6 of `x - 7//2` of `3//7` equals `- 7//4,` then the value of x is

Options

A. `-1.5`
B. 3
C. `-2.5`
D. 6

Answer

To solve the equation given in the question, we will follow these steps:

### Step 1: Write the equation based on the problem statement
We start with the equation:
\[ \frac{1}{6} \left( x - \frac{7}{2} \cdot \frac{3}{7} \right) = -\frac{7}{4} \]

### Step 2: Simplify the expression inside the parentheses
First, we simplify \(\frac{7}{2} \cdot \frac{3}{7}\):
\[ \frac{7}{2} \cdot \frac{3}{7} = \frac{7 \cdot 3}{2 \cdot 7} = \frac{3}{2} \]
Now substitute this back into the equation:
\[ \frac{1}{6} \left( x - \frac{3}{2} \right) = -\frac{7}{4} \]

### Step 3: Eliminate the fraction by multiplying both sides by 6
To eliminate the fraction, multiply both sides by 6:
\[ x - \frac{3}{2} = 6 \cdot -\frac{7}{4} \]
Calculating the right side:
\[ 6 \cdot -\frac{7}{4} = -\frac{42}{4} = -\frac{21}{2} \]
So now we have:
\[ x - \frac{3}{2} = -\frac{21}{2} \]

### Step 4: Isolate x
To isolate \(x\), add \(\frac{3}{2}\) to both sides:
\[ x = -\frac{21}{2} + \frac{3}{2} \]
Combining the fractions:
\[ x = \frac{-21 + 3}{2} = \frac{-18}{2} = -9 \]

### Step 5: Conclusion
Thus, the value of \(x\) is:
\[ x = -9 \]

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