C1- Algebra and Functions - Solving Quadratic and Linear Inequalities

Now we move on to Solving Inequalities. An Inequality is basically a statement comparing to variables, usually about their size. e.g. a < b (a is less than b - the value of a is less than b)

let  x = john's weight and y = rahul's weight
x < y (john's weight is less than rahul's weight)

Let's recap the different signs used in inequalities :

> is more than
< is less than
These are known as STRICT Inequalities. e.g. 7 < 13 is a strict inequality ( 7 is strictly less than 13) [This is not in the spec. - but it may be useful later on]
≥ is more than or equal to
≤ is less than or equal to. 

Rules of Inequalities

1) We are allowed to add or subtract the same number on both sides.
2) We are allowed to switch sides, and change the sign.


e.g.   4 < 5-x is the same as 5-x > 4.


3) We are allowed to multiply by the same number on both sides, But if this number is positive, the sign remains the same, if it is negative the sign has to be reversed.


e.g   [6 > 3x + 4 ] * 3 =   [18 > 9x + 12]
        [6 > 3x - 4 ] *-2 =   [-12<-6x + 8]


We we looked at so far, are examples of LINEAR Inequalities.

Solving Linear Inequalities Notes

Quadratic Inequalities 

1) Simplify this Quadratic Inequality, to get one quadratic expression. Rearrange the inequality to get it equal to 0. ( > 0, < 0 or less than equal to or more than equal to).
2) Find the roots of the equation (Solve the quadratic). The roots are called CRITICAL VALUES.
3) Draw the graph of the equation, seeing which x values satisfy the inequality,using the Critical Values.

Solving Quadratic Inequalities Notes