January 10th

Inequalities
As you already know, we use the following symbols:


Solving inequalities
"Solving'' an inequality means finding all of its solutions. A "solution'' of an inequality is a number which when substituted for the variable makes the inequality a true statement.
For example: 2 is a solution of 2x-3<5 because 2·2-3<5

When solving inequalities, there are certain manipulations of the inequality which do not change the solutions:

Rule 1. Adding/subtracting the same number on both sides.

Rule 2. Multiplying/dividing by the same POSITIVE number on both sides.

Rule 3. Multiplying/dividing by the same NEGATIVE number on both sides AND changing the orientation of the inequality sign.

ALWAYS EXPRESS SOLUTIONS AS AN INTERVAL(S)