Absolute value of any number or expression must be positive.
If (x-4) is positive then |x-4| is also positive
What if x-4 is negative? Since the absolute value must be positive, |x-4| would be equal to -(x-4)=4-x.
Right?
We know that x-4 would have to be negative for the equation in question to be true. This would imply that x would have to be a small positive number smaller than 4 or a negative number. You can take examples to test that.
x=-14 (x-4)=-ve
x=1, x-4=-3 -ve
x=4, implies x-4=0 and 4-x=0. Thus, the equation is satisfied.
Hence, d is the answer.
Coming to your question, if a question deals with equality it also indirectly deals with inequality. If you say the equation is satisfied when x=0,x=4,x=-5 and so on, it also implies that the equation is true for all values of x less than or equal to 4.
An equation exists only at certain points. We have to find those points and if those points range over a large space, the easiest way would be express it as inequality.
Note: An equality question can have answers which might be expressed as inequalities. There is nothing wrong with it.
Hope it helps! Let me know if I can help you any further.
dhlee922 wrote:
how come all of a sudden the answer has inequalities when the question only had equal signs? that's the part i dont understand