1. Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not?
Write an inequality to be solved with the answer. In your inequality, use both the multiplication and addition properties of inequalities.
2. How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.
If you look at the inequality 6>3, that means 6 is a bigger number than 3. However, if you multiply (-1) to both sides of the inequality, you should change the sign, which leads to
-6<-3, since -6 is a smaller number than -3. If you want to compare two negative numbers, the bigger the absolute value is, the smaller the number is.
It does not happen in equation, because the equality sign does not have direction. For example, x=-2 is the same as –x=2
Example of solving inequality
Multiplying both sides by (-2), we have
Adding both sides ...
This provides explanations of working with inequalities, included in a Word document file and worked through step by step.