Question

do you reverse the inequality?

Answer 1

The inequality reverses in specific cases, such as:

1. **Multiplying or dividing by a negative number**: If you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. For example:

\[
-2x > 6 \quad \text{(divide both sides by -2)}
\]
becomes:
\[
x < -3
\]

2. **Rearranging the terms**: If you subtract or add the same value on both sides of the inequality, the direction of the inequality remains the same. For example:

\[
3 > 2 \quad \text{(subtracting 1 from both sides)}
\]
remains:
\[
2 > 1
\]

3. **Taking the reciprocal of both sides**: If both sides of the inequality are positive and you take the reciprocal, the inequality sign will reverse. For example:

\[
2 > 1 \quad \text{(taking reciprocals)}
\]
becomes:
\[
\frac{1}{2} < 1
\]

4. **When comparing with absolute values**: The behavior can differ unless specified under certain conditions.

Always consider the context of the inequality when determining if the sign needs to be reversed.