Contents

Introduction

Properties

Linear Inequalities 

1  2

Quadratic Inequalities 

Cubic Inequalities

Fractional Inequalities

Modulus Inequalities

Problem Solving

Quiz 

Algebra Main Page

Solving Quadratic Inequalities

An inequality with a quadratic expression in one variable on one side and zero on the other, is called a quadratic inequality in one variable. For example,

(x - 1)(x - 4) < 0

is a quadratic inequality in x, The range of value of x which satisfies this inequality can solved as follow:

For (x - 1)(x - 4) < 0 (i.e. y is negative), we choose the interval for which the curve is below the x-axis.

1 < x < 4.

Similarly, if (x - 1)(x - 4) > 0 (i.e. y is positive) we choose the interval for which the curve is above the x-axis.

x < 1 or x > 4.

Example 2

Find the range of value of x for which 2x² < 5x + 3.

            2x² < 5x + 3

    2x² - 5x - 3 < 0

(2x + 1)(x - 3) <0

-½ < x < 3

Example 3

Find the inequality to the inequality, 4x(x + 1) 3.

         4x(x + 1) 3

     4x² + 4x - 3 0

(2x - 1)(2x + 3) 0

the solution is -3/2 x  or x ½.