# High School Math : Understanding Absolute Value

## Example Questions

### Example Question #1 : Mathematical Relationships And Basic Graphs

Expression 1: Expression 2: Find the set of values for where Expression 1 is greater than Expression 2.

All values where All real numbers

All values where All values where All values where All values where Explanation:

In finding the values for where , break the comparison of these two absolute value expressions into the four possible ways this could potentially be satisfied.

The first possibility is described by the inequality: If you think of a number line, it is evident that there is no solution to this inequality since there will never be a case where subtracting from will lead to a greater number than adding to .

The second possibility, wherein is negative and converted to its opposite to being an absolute value expression but is positive and requires no conversion, can be represented by the inequality (where the sign is inverted due to multiplication by a negative): We can simplify this inequality to find that satisfies the conditions where .

The third possibility can be represented by the following inequality (where the sign is inverted due to multiplication by a negative): This is again simplified to and is redundant with the above inequality.

The final possibility is represented by the inequality This inequality simplifies to . Rewriting this as makes it evident that this inequality is true of all real numbers. This does not provide any additional conditions on how to satisfy the original inequality.

The only possible condition that satisfies the inequality is that which arises in two of the tested cases, when .

### Example Question #1 : Mathematical Relationships And Basic Graphs

What is the absolute value of -3?

-3

1

9

3

10 