find the value of x`(-3)/(14) *x=(5)/(12)`

Options

A. `(-35)/(18)`
B. `(35)/(18)`
C. `(7)/(3)`
D. `(-7)/(3)`

Answer

To solve the equation \(-\frac{3}{4} \cdot x = \frac{5}{12}\), we need to isolate \(x\). Here’s the step-by-step solution:

### Step 1: Write the equation
We start with the equation:
\[ -\frac{3}{4} \cdot x = \frac{5}{12} \]

### Step 2: Isolate \(x\)
To isolate \(x\), we need to eliminate the coefficient \(-\frac{3}{4}\) from the left side. We can do this by multiplying both sides of the equation by the reciprocal of \(-\frac{3}{4}\), which is \(-\frac{4}{3}\):
\[ x = \frac{5}{12} \cdot \left(-\frac{4}{3}\right) \]

### Step 3: Multiply the fractions
Now, we multiply the fractions on the right side:
\[ x = \frac{5 \cdot (-4)}{12 \cdot 3} \]
This simplifies to:
\[ x = \frac{-20}{36} \]

### Step 4: Simplify the fraction
Next, we simplify \(\frac{-20}{36}\). We can divide both the numerator and the denominator by their greatest common divisor, which is 4:
\[ x = \frac{-5}{9} \]

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

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