Answer: |4x-2|=-6 has no solutions.
This is because the absolute value equation is equal to a negative value. This cannot occur because absolute value is the distance from 0, and distance is always a positive measurement. Thus, absolute value always produces a positive output. For example, if we were to find the absolute value of 6, it would look like:
|x|=6
So, x must be two numbers that are 6 units from 0; there is a positive and negative value, but the negative value turns positive since there is no negative distance.
Thus, we’d know that x=-6, 6 because |-6|=6 and |6|=6, so -6 is 6 units from 0 and 6 is 6 units from 0.
However, what if we said the absolute value of a number, x, must equal -6? Well, here’s what happens:
|x|=-6
|-6|≠-6 and |6|≠-6
So, there are no solutions to this equation because distance can’t negative. There is no value that is -6 units from 0.