What is the solution set for StartAbsoluteValue y minus 9 EndAbsoluteValue less-than-or-equal-to 12:A? y greater-than-or-equal-to 3 or y less-than-or-equal-to 21
Negative 3 less-than-or-equal-to y less-than-or-equal-to 21
y greater-than-or-equal-to negative 3 or y less-than-or-equal-to 21
3 less-than-or-equal-to y less-than-or-equal-to 21

Using the absolute value concept, it is found that the solution is:

Which is given by the second option.

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The absolute value of a point, or of a function, measures it's distance to the origin.The inequality given by:

The distance to the origin is of at most 12 between -12 and 12, thus:

We have to solve both inequalities, and find the intersection.

The intersection is values of y between -3 and 21(and logical operator, not or), inclusive, thus: and , that is:

A similar problem, involving absolute value, is given at link