| 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 ³ - 5 \ x £ 3 and 2 x ³ - 4
x ³ - 2 \ x £ 3 and x ³ -2 or - 2 £ x Therefore , - 2 £ x £ 3 . . . required solution = [ - 2 , 3 ]
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7.1 Definition |
