Question

What is meant by strictly addictive properties of a solution?

Answer 1

Let's start with the following true inequality:

10 < 20

Next, we will add -5 to each side of the equation as follows:

10 + (-5) < 20 + (-5)

Finally, simplify to get the following:

5 < 15

The inequality still holds true as expected. Notice that we can use subtraction within the additive properties by adding a negative number. Let's try an example with one variable:

x - 25 > 55

We want to solve for x, so we can use the additive property of inequalities and add 25 to both sides of the inequality and simplify:

x - 25 + 25 > 55 + 25

x > 80

While solving the above inequality, and the equation earlier, we were using another basic property of algebra called the additive inverse property.

Definition: Additive Inverse Property

The additive inverse of any number a is -a. If we add these terms together we get zero:

a + (-a) = 0