Final answer:
Inequalities and absolute values are used to compare magnitudes or analyze piecewise functions. The direction of inequality may change depending on the evaluation of the variable inside the absolute value. Understanding these concepts is crucial for interpreting and solving mathematical problems involving inequalities and absolute values.
Step-by-step explanation:
The question pertains to understanding how to use inequality signs when dealing with absolute values and piecewise functions. When an absolute value function is expressed in piecewise form, inequality signs change depending on whether the variable inside the absolute value is positive or negative. For example if the inside is positive, the inequality remains the same as the absolute value symbol is redundant.
However when the inside is negative, the inequality sign will flip because we'll be multiplying by -1 to get rid of the absolute value which reverses the direction of the inequality. In a typical comparison of magnitudes using inequalities (like comparing forces or areas) we often have to determine which one is greater or whether they are equal.