Find the value of x .`(4)/(3) divide x =(-5)/(2)`

Options

A. `(-8)/(5) `
B. `(8)/(5)`
C. `(-8)/(15)`
D. `(8)/(15)`

Answer

To solve the equation \( \frac{4}{3} \div x = -\frac{5}{2} \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{4}{3} \div x = -\frac{5}{2} \]

### Step 2: Eliminate the division by multiplying both sides by \( x \)
To eliminate the division by \( x \), we can multiply both sides of the equation by \( x \):
\[ \frac{4}{3} = -\frac{5}{2} \cdot x \]

### Step 3: Isolate \( x \)
Now, we want to isolate \( x \). To do this, we can divide both sides by \( -\frac{5}{2} \):
\[ x = \frac{4}{3} \div -\frac{5}{2} \]

### Step 4: Change division to multiplication
Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we can rewrite the equation as:
\[ x = \frac{4}{3} \cdot -\frac{2}{5} \]

### Step 5: Multiply the fractions
Now, we multiply the fractions:
\[ x = \frac{4 \cdot -2}{3 \cdot 5} = \frac{-8}{15} \]

### Final Answer
Thus, the value of \( x \) is:
\[ x = -\frac{8}{15} \]

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