Linear and Quadratic Functions: Solving Linear Equations and Inequalities

Properties of Inequalities

Just like with linear equations, there are properties of inequalities we need to go through before we can solve linear inequalities.

Properties of Inequality

For all real numbers a, b, and c, where a ≤ b:

Addition Property

a + c ≤ b + c

Subtraction Property

a – c ≤ b – c

Multiplication Property

If c ≥ 0, then ac ≤ bc
If c ≤ 0, then ac ≥ bc

Division Property

If c > 0, then a divided by c is less than or equal to b divided by c
If c < 0, then  a divided by c is greater than or equal to b divided by c

 

The big concept to notice and remember is that when you multiply or divide an inequality by a negative number, the direction of the inequality changes.