What happens to the inequality symbol when you do the following to each side of an inequality?
1. Subtract a negative number
nothing happens
If you multiply or divide both sides by a negative number, the direction of the arrow must change.
eg:
3 < 4
-3 < -4 NO
-3 > -4
When you subtract a negative number from both sides of an inequality, you are essentially adding a positive number. To understand the property involved, let's take a closer look at an example inequality:
5 > 3
If we subtract -2 from both sides, the inequality becomes:
5 - (-2) > 3 - (-2)
Simplifying this, we get:
5 + 2 > 3 + 2
Which further simplifies to:
7 > 5
From this, we can observe that the inequality symbol remains the same (>) when we subtract a negative number from both sides.
To summarize, subtracting a negative number is equivalent to adding a positive number, and it does not change the direction of the inequality.