Find the absolute-value inequality statement that corresponds to the inequalities x < 19 or x > 24.
|x| > a implies that x > a or x < -a Think of absolute value is the distance between x and 0. There is symmetry between 0 and a.
The idea for this is that we need to shift 0 to a point that gives us similar symmetry with 19 and 24. Drawing a number line may help. On a number line, the mid point between 19 and 24 is 21.5 and it is 2.5 units from both 19 and 24.
So examine |x - 21.5| >= 2.5. You'll see the same symmetry. I'm having a hard time explaining it, but hopefully there is enough here to understand the process.
