Question

In solving inequality, why do we need to flip/change the inequality sign when multiplying or dividing both sides of the inequality by a negative value?

Option 1: It's a mathematical rule.
Option 2: To confuse the reader.
Option 3: To make the inequality easier to solve.
Option 4: It's an arbitrary convention.

Answer 1

When we multiply or divide both sides of an inequality by a negative value, we need to flip or change the inequality sign to ensure that the inequality still holds true when dealing with negative values.

Step-by-step explanation:

When we multiply or divide both sides of an inequality by a negative value, we need to flip or change the inequality sign. This is because negative numbers have a different relationship with multiplication and division compared to positive numbers. When we multiply or divide two positive numbers, the resulting answer is positive. When we multiply or divide two negative numbers, the answer is also positive. However, when we multiply or divide a positive number with a negative number, the answer is negative. Flipping the sign ensures that the inequality still holds true when dealing with negative values.

For example, let's say we have the inequality -3 < 2. If we divide both sides by -1, we need to flip the sign and the inequality becomes 3 > -2, which is still true.