Dividing inequality

Question

Determine if the following statement is true or false.

Dividing each side of an inequality by−4 reverses the direction of the inequality.
Choose the correct answer below.

A.
True, if both sides of an inequality are multiplied or divided by the same positive number, the inequality sign must be reversed to have an equivalent inequality.

B.
True, if both sides of an inequality are multiplied or divided by the same negative number, the inequality sign must be reversed to have an equivalent inequality.

C.
False, if both sides of an inequality are multiplied or divided by the same negative number, the inequality sign must stay the same to have an equivalent inequality.

D.
False, if both sides of an inequality are multiplied or divided by the same positive number, the inequality sign must stay the same to have an equivalent inequality.

Answer 1

The answer is B.  If you multiply or divide both sides of an inequality by a negative number, it reverses the inequality.  This is an important rule that you need to remember when working with inequalities.

 

Example:

 

-4x > 24

 

-4x/-4 < 24/-4      (Divide both sides by -4, so the > changes to <)

 

x < -6