# Section 1.3

- Page ID
- 23212

Main difference #1:

Linear Equations typically have 1 solution (they can have none, or an infinite amount as well).

Linear Inequalities will typically have an infinite amount of solutions.

Consider the inequality \(x > 5\). How many numbers do you know that would satisfy x?

Some examples of numbers greater than 5 are: 6, 7.8, 9000, 463, etc.

There are an infinite amount of solutions!

Thus, when we express the solution set for an inequality, we must write it with an inequality and

in interval notation, to show all the numbers in the solution.

Main difference #2:

Recall when we talked about solving linear equations, we used two properties: the additive

property of equality, and the multiplicative property of equality. The additive property of equality

holds for inequalities, however the multiplicative property of equality does NOT always hold for

inequalities.

Why? Well, let’s consider the following example: 9 > 4. If we were to multiply both side of this

inequality by 2, will it still be true? Let’s try it: 9(2) > ? 4(2), is equal to saying 18 > 8. Sure, it's still

true, 18 is greater than 8.