# Inequalities

Notes on inequalities

- Created by: Natasha Naeem
- Created on: 10-06-11 13:53

First 287 words of the document:

Additional Mathematics

Algebra: Techniques

Section 1: Linear and quadratic inequalities

Notes and Examples

These notes contain subsections on

Linear inequalities

Quadratic inequalities

Linear inequalities

You already know that y = 2x + 1 is a straight line but what happens if we need

to look at y 2x + 1 or y 2x + 1. If you draw the line and then move a ruler

upwards parallel to it, the values of x + 1 will not change but the corresponding

y values will be bigger. Similarly if you move the ruler down from the line, x + 1

will stay the same but the y values will be smaller; i.e. points above the line

will satisfy y 2x + 1 and those below the line will satisfy y 2x + 1. To solve

inequalities we follow the same procedure as for solving equations except

when we multiply or divide by a negative number. In this case the direction of

the inequality reverses. E.g. 4 2 but if we multiply by 1, 4 is not greater

than 2, but less than 2.

It is best to try and avoid dividing by a negative as in the following example.

Add x to both sides

7 15 x

7 + x 15 Take 7 away from both sides

x8

Doing the inequality in this way meant that we weren't left with: 8 x and

the need to multiply or divide by 1.

Example 1

Solve:

(i) 2x 3 9

(ii) 6y + 1 4y + 9

(iii) 11 3x + 5 20

Solutions

(i) 2x 3 9

2x 12

x6 Collect like terms i.e. take

4y away from both sides

(ii) 6y + 1 4y + 9

2y + 1 9

Take 1 from both sides

© MEI, 24/07/09 1/3

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