In an equation does the inequality sign change when both sides are multiplied or divided by a negative number? Why or why not?

See first post. Thanks for asking.

yes, the inequality sign changes because the negative signs change

Yes, the inequality sign does change when both sides of an equation are multiplied or divided by a negative number.

When we multiply or divide both sides of an equation by a positive number, the direction of the inequality is preserved. However, when we multiply or divide both sides by a negative number, the direction of the inequality is reversed.

To understand why this happens, let's consider an example. Suppose we have the inequality 3 > 2. If we multiply both sides by a positive number, let's say 4, we get 12 > 8, which is still true. However, if we multiply both sides by a negative number, let's say -4, we get -12 > -8, which is not true. In this case, the sign changed because we multiplied both sides by a negative number.

The reason for this is that multiplying or dividing by a negative number flips the number line. It swaps the positions of the positive and negative numbers. As a result, the direction of the inequality needs to be reversed to reflect this change.

In summary, when you multiply or divide both sides of an equation by a negative number, you must reverse the direction of the inequality sign. This ensures that the inequality remains true in the new equation.