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 ?
Whether to use 'OR' or 'AND'
1
$\begingroup$
terminology
-
0The question is a bit too generic. Could you gives us some equations/inequalities you have encountered? We could then help you understand accordingly. – 2012-06-04
-
0@Marvis-example:|x-4|=1 , |x-4|is less than or equal to 2 – 2012-06-04
1 Answers
2
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 $x-4 \le 2$
-
0ok... thanks i got it – 2012-06-04
-
0does |x-4|=o means that x is such a point which is zero distance away from 4? – 2012-06-04
-
0@meg_1997: Yes. When an absolute value is zero, you can just remove the absolute value signs. $|y|=0$ is the same as $y=0$ because there is only one number with absolute value $0$. – 2012-06-04
-
0please will you tell whether to use the conjunction 'OR'or 'AND'? in example: |p| is greater than or equal to4 – 2012-06-04
-
0@meg_1997: what values of $p$ make $|p| \ge 4$? – 2012-06-04
-
0-5,-4,.... and 4,5.... – 2012-06-04
-
0@meg_1997:So you have two classes of solution. Look back at the original definition and see if you can figure it out. – 2012-06-04
-
0should i use 'OR'? – 2012-06-04
-
0@meg_1997: yes, you have $p \le -4$ OR $p \ge 4$ – 2012-06-04
-
0@ Ross Miilikan : ok, hey will u please see my question here http://math.stackexchange.com/questions/153681/absolute-value-on-a-number-line#comment354240_153681 – 2012-06-04