The important thing to remember in this situation is that the absolute value can never be negative. The most basic rule of absolute values can be shown as:
|a|=a and |- a|=a.
For this exercise, we can ignore everything inside the absolute value symbols and just look at the fact that we have the absolute value of something is greater than or equal to a negative number.
|...|≥-6
No matter what value of x we substitute into the expression 4x-2, whether it gives a positive or negative result, the absolute value will make it where the left-hand side is always a positive number. A positive number will always be greater than a negative number. Hence, the solution is that the inequality is true for all real numbers.
