If a, b and c are real numbers such that a < b and `clt0`, then of the statements which is true?

Options

A. `a/c lt b/c`
B. `ac lt bc`
C. `c/a gt c/b`
D. `ac gt bc`

Answer

To solve the problem, we need to analyze the given conditions and apply the properties of inequalities when multiplying by a negative number.

### Step-by-Step Solution:

1. **Understand the Given Conditions**:
We know that:
- \( a < b \) (i.e., \( a \) is less than \( b \))
- \( c < 0 \) (i.e., \( c \) is a negative number)

2. **Multiply the Inequality by the Negative Number**:
Since \( c \) is negative, we can multiply both sides of the inequality \( a < b \) by \( c \). However, we must remember that when we multiply both sides of an inequality by a negative number, the direction of the inequality reverses.

Therefore, multiplying \( a < b \) by \( c \):
\[ a \cdot c > b \cdot c \]
This means that \( ac \) is greater than \( bc \).

3. **Conclusion**:
The final result we derived is:
\[ ac > bc \]
This means that the statement \( ac > bc \) is true under the given conditions.