Problem

Assume that $\mathrm{a}< \mathrm{b}$ and $\mathrm{c}< 0$. State whether the following statement is true or false
\[
a c> b c
\]

Answer

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Answer

Final Answer: The statement \(ac > bc\) is \(\boxed{true}\) when \(a < b\) and \(c < 0\).

Steps

Step 1 :Assume that \(abc\).

Step 2 :This is a question about the properties of inequalities. When we multiply or divide both sides of an inequality by a positive number, the direction of the inequality remains the same. However, when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality changes.

Step 3 :Since \(c\) is less than 0, it is a negative number. Therefore, when we multiply both sides of the inequality \(a < b\) by \(c\), the direction of the inequality should change.

Step 4 :So, the statement \(ac > bc\) should be true.

Step 5 :Final Answer: The statement \(ac > bc\) is \(\boxed{true}\) when \(a < b\) and \(c < 0\).

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