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 \(\frac{1}{6}x - \frac{7}{2} \cdot \frac{3}{7} = -\frac{7}{4}\), we will follow these steps:

### Step 1: Simplify the term \(\frac{7}{2} \cdot \frac{3}{7}\)

First, we can simplify \(\frac{7}{2} \cdot \frac{3}{7}\):
\[ \frac{7}{2} \cdot \frac{3}{7} = \frac{7 \cdot 3}{2 \cdot 7} = \frac{3}{2} \]

### Step 2: Substitute the simplified term back into the equation

Now, we substitute this back into the equation:
\[ \frac{1}{6}x - \frac{3}{2} = -\frac{7}{4} \]

### Step 3: Isolate \(\frac{1}{6}x\)

To isolate \(\frac{1}{6}x\), we add \(\frac{3}{2}\) to both sides:
\[ \frac{1}{6}x = -\frac{7}{4} + \frac{3}{2} \]

### Step 4: Find a common denominator

To add \(-\frac{7}{4}\) and \(\frac{3}{2}\), we need a common denominator. The least common multiple of 4 and 2 is 4. We convert \(\frac{3}{2}\) to have a denominator of 4:
\[ \frac{3}{2} = \frac{3 \cdot 2}{2 \cdot 2} = \frac{6}{4} \]

### Step 5: Perform the addition

Now we can add:
\[ -\frac{7}{4} + \frac{6}{4} = \frac{-7 + 6}{4} = \frac{-1}{4} \]

### Step 6: Substitute back into the equation

Now we have:
\[ \frac{1}{6}x = -\frac{1}{4} \]

### Step 7: Solve for \(x\)

To solve for \(x\), we multiply both sides by 6:
\[ x = 6 \cdot -\frac{1}{4} = -\frac{6}{4} = -\frac{3}{2} \]

### Step 8: Convert to decimal

Converting \(-\frac{3}{2}\) to decimal gives:
\[ -\frac{3}{2} = -1.5 \]

### Final Answer

Thus, the value of \(x\) is \(-1.5\).

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