## Solving inequalities and multiplying or dividing by a negative number requires this

### When solving inequalities and multiplying or dividing by a negative number, it is important to remember the concept of reversing the inequality sign

When solving inequalities and multiplying or dividing by a negative number, it is important to remember the concept of reversing the inequality sign.

Here’s why:

1. Multiplying or dividing by a positive number:

– If you multiply or divide both sides of an inequality by a positive number, the inequality sign remains the same.

– For example, if you have the inequality 2x > 6 and you divide both sides by 2 (which is positive), the inequality remains the same and you get x > 3.

2. Multiplying or dividing by a negative number:

– When you multiply or divide both sides of an inequality by a negative number, you need to reverse the inequality sign.

– For example, if you have the inequality -3x > 9 and you divide both sides by -3 (which is negative), you must reverse the inequality sign and get x < -3.
This reversal of the inequality sign occurs because multiplying or dividing by a negative number changes the direction of the number line. It flips the positive and negative sides of the numbers, which means the relationship between the values represented by the inequality symbol needs to be reversed.
Therefore, when solving inequalities and encountering multiplication or division by a negative number, always remember to reverse the inequality sign.

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