Linear Inequalities

Success Criteria

At the end of this chapter, students are able to:

1. Solve simple linear inequalities.

2. Solve simultaneous linear inequalities.

3. Represent the solution of linear inequalities on a number line.

4. Solve real world problems involving linear inequalities (AO2).

5. Justify whether a linear inequality statement is true or false (AO3).

The Law of Trichotomy

The law states that all real numbers are either less than zero, more than zero or zero itself.

i.e, x < 0 or x > 0 or x = 0

Similarly, for any 2 real numbers (A & B), one must either be greater than the other or else they would be equal.

i.e, A < B or A > B or A = B

Basic Properties of Inequalities

Addition Property: If a < b ⇒ a + c < b + c

Subtraction Property: If a < b ⇒ a − c < b − c

Multiplication Property: If a < b ⇒ ac < bc (if c > 0), ac > bc (if c < 0), ac = bc (if c = 0).

Division Property: Same as multiplication.