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My doubt is: while solving equations or inequalities consisting of absolute values when should we use the conjunction 'OR' and when to use 'AND'? whats the difference between them ?

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    @Marvis-example:|x-4|=1 , |x-4|is less than or equal to 22012-06-04

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OR means one (or more) of the choices must be true; AND means they must all be true. In each case you need to think which you need. For your examples, $|x-4|=1$ is true whenever $x-4$ is 1 OR -1. $|x-4|\le 2$ is only true when $-2 \le x-4 \le 2$, so you must have $-2 \le x-4$ AND $x-4 \le 2$

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    @ Ross Miilikan : ok, hey will u please see my question here http://math.stackexchange.com/questions/153681/absolute-value-on-a-number-line#comment354240_1536812012-06-04