lj_neary Wrote:Can someone please post a step by step explanation of how statement 2 is simplified into x<0. Thanks.
Sure. Here's the statement:
(2) |x| > x
Let's think about this. The absolute value of x, |x|, is always the positive distance from x to zero on the number line. So unless x itself is zero, |x| will always be positive.
Can x itself be positive? Can x be something such as 3? Well, no, because |3|=3, and thus |3| is not greater than 3, as our statement says.
Can x be zero? No, because the two sides would both be zero; the left is not greater than the right.
Can x be negative? Yes! If x is something such as -2, note that |-2|=2, and 2 > -2. The absolute value transforms the left to a positive number, but the right is left as a negative number. Note that this works for any negative number.
I hope this helps!