Find the value of `(9abs(3-5)-5abs4div10)/(-3(5)-2xx4div2)`

Options

A. `9/10`
B. `-8/17`
C. `-(16)/19`
D. `4/7`

Answer

To solve the expression \((9 \cdot |3-5| - 5 \cdot |4| \div 10) / (-3 \cdot 5 - 2 \cdot 4 \div 2)\), we will follow these steps:

### Step 1: Calculate the absolute values
First, we need to calculate the absolute values in the expression:
- \( |3 - 5| = | -2 | = 2 \)
- \( |4| = 4 \)

### Step 2: Substitute the absolute values into the expression
Now, we substitute the absolute values back into the expression:
\[ (9 \cdot 2 - 5 \cdot 4 \div 10) / (-3 \cdot 5 - 2 \cdot 4 \div 2) \]

### Step 3: Simplify the numerator
Next, we simplify the numerator:
- Calculate \(9 \cdot 2 = 18\)
- Calculate \(5 \cdot 4 = 20\)
- Now divide \(20 \div 10 = 2\)
- So, the numerator becomes \(18 - 2 = 16\)

### Step 4: Simplify the denominator
Now, we simplify the denominator:
- Calculate \(-3 \cdot 5 = -15\)
- Calculate \(2 \cdot 4 = 8\)
- Now divide \(8 \div 2 = 4\)
- So, the denominator becomes \(-15 - 4 = -19\)

### Step 5: Combine the results
Now we can combine the results:
\[ \frac{16}{-19} \]

### Step 6: Final result
Thus, the final result is:
\[ -\frac{16}{19} \]