Contents

Introduction

Properties

Linear Inequalities 

1  2

Quadratic Inequalities 

Cubic Inequalities

Fractional Inequalities

Modulus Inequalities

Problem Solving

Quiz 

Algebra Main Page

Problem Solving involving Inequalities

We shall look at how inequalities can be used to solve problems.

Example 1

Peter and his younger brother want to buy a present for their mother. Peter agrees to pay $4 more than his brother. If the present does not cost more than $30, what is the greatest possible amount paid by Peter?

Let x be the amount paid by Peter.

brother pay $(x-4).

x + x - 4 30

         2x 34

           x 17

The greatest amount paid by Peter is $17.

Example 2

James scored 66 and 72 marks in two class tests. What is the lowest mark he must score for the third test to qualify for a bonus prize is an average score of 75 is needed to qualify for the prize?

Let x be the mark for the third test.

(66 + 72 + x )/3 75

    66 + 72 + x 75 x 3

                      x 225 - 66 - 72

                      x 87

James must score at least 87 marks.                

Example 3

A Mathematics test consists of 20 multiple-choice questions. A correct answer is awarded 3 marks and one mark is deducted for every wrong answers. No marks are awarded or deducted for questions not attempted. A boy attempted a total of 19 questions and his total score for the test was above 32. Find the minimum number of correct answers he obtained.

Let x be the number of correct answers and y the number of incorrect answers.

            x + y = 19 --------(1)

            3x - y = 32 --------(2)

From (1): y = 19 - x --------(3)

Subst.(3) into (2): 3x - (19 - x) > 32

                             3x - 19 +x > 32

                                         4x > 41

                                           x > 12.75

Since x must be a whole number, the minimum number of questions he answered correctly was 13.