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Solving inequalities and graphing

Example    Solve and graph 2 | x + 2 | > 6

Solution :    i) Isolate the absolute value as | x + 2 | > 3

ii) Setting the contents of the absolute value portion to + 3 and - 3 or

+ (x + 2) > 3 and - ( x + 2) > 3

\ x + 2 > 3 and x+2 < -3

x > 1 and x < -5

The graph is

Example     Solve and graph | 2 x - 1 | £ 5

Solution :     | 2 x - 1 | £ 5

Therefore, setting the contents pf the absolute value portion as

( 2 x - 1 ) £ + 5 and - ( 2 x - 1) £ + 5

\ 2 x £ 6 and 2 x - 5

\ x £ 3 and 2 x ≥ - 4

x ≥ - 2

\ x £ 3 and x ≥ -2 or - 2 £ x

Therefore , - 2 £ x £ 3 . . . required solution

= [ - 2 , 3 ]

Index

7.1 Definition
7.2 Simultaneous Equations
7.3 Inequations (Inequalities)
7.4 Absolute Values

Chapter 8

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