Question

When solving inequalities, under what condition should you flip the inequality sign?

a) Always flip the sign when dividing
b) Never flip the sign when dividing
c) Flip the sign when dividing by a negative number
d) Flip the sign when multiplying

Answer 1

Flip the inequality sign when dividing by a negative number. This preserves the correct order relationship in inequalities during the operation.

Step-by-step explanation:

When solving inequalities, you should flip the inequality sign under the condition when you are dividing by a negative number. It's important to note that you don't flip the sign when dividing by a positive number or when multiplying, unless the multiplication is by a negative number.

The rules for multiplication and division regarding signs follow that of basic arithmetic, where multiplying or dividing two positive numbers results in a positive answer, and doing the same with two negative numbers will also yield a positive answer. However, when you combine a positive and a negative number through multiplication or division, the result will be negative. The flipping of the inequality sign preserves the order relationship.

For instance, if -2 is multiplied to both sides of the inequality x > 3, the inequality sign must be flipped, resulting in -x < -6, maintaining the true value of the original inequality.