The sum of `(7)/(-3) and (5)/(-6)` is equal to the product of `(-4)/(11)` and a number. Find the number.

Options

A. `5 (7)/(11) `
B. `8 (17)/(24)`
C. `-3 (1)/(6)`
D. `1 (5)/(33)`

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript and break down the calculations clearly.

### Step 1: Write the equation
We need to find the number \( x \) such that:
\[ \frac{7}{-3} + \frac{5}{-6} = \frac{-4}{11} \times x \]

### Step 2: Calculate the left-hand side (LHS)
We need to add the fractions \( \frac{7}{-3} \) and \( \frac{5}{-6} \). To do this, we need a common denominator. The least common multiple (LCM) of 3 and 6 is 6.

- Convert \( \frac{7}{-3} \) to have a denominator of 6:
\[ \frac{7}{-3} = \frac{7 \times 2}{-3 \times 2} = \frac{14}{-6} = \frac{-14}{6} \]

- Now we can add the two fractions:
\[ \frac{-14}{6} + \frac{5}{-6} = \frac{-14 - 5}{6} = \frac{-19}{6} \]

### Step 3: Set up the equation
Now we have:
\[ \frac{-19}{6} = \frac{-4}{11} \times x \]

### Step 4: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ -19 \times 11 = -4 \times 6 \times x \]
This simplifies to:
\[ -209 = -24x \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by -24:
\[ x = \frac{209}{24} \]

### Final Answer
Thus, the number is:
\[ \boxed{\frac{209}{24}} \]