MATH117 Lecture Notes - Lecture 6: Oliver Heaviside, Bes, Function Composition
18 Dec 2015
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At a basic level, it is obvious to solve for x. When working with inequalities on the other hand, you need to be a little more careful (i. e. negatives ipping the direction, etc. ). This forces us to consider 4 potential cases for the values of x we need to solve! Find all values (i. e. cases) of x which satisfy the following inequality: By convention, we assume that there are 4 di erent possibilities for x, as we can split up the inequality into. |x 3| |2x + 8| (1) x 3 2x + 8. (x 3) 2x + 8 x 3 (2x + 8) (2) (3) (4) (5) But if we look at the number line, one of these cases does not make any sense! Clearly, it is impossible for x > 3 and x < 4 at the exact same time! So we are able to discard the fourth case and work with just the rst 3 cases:
