High School Math : Understanding Absolute Value

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #4 : Mathematical Relationships And Basic Graphs

Expression 1: 

Expression 2: 

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

Possible Answers:

All values where 

All values where 

All values where 

All values where 

All real numbers

Correct answer:

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 : Understanding Absolute Value

What is the absolute value of -3? 

Possible Answers:

9

-3

10

1

3

Correct answer:

3

Explanation:

The absolute value is the distance from a given number to 0. In our example, we are given -3. This number is 3 units away from 0, and thus the absolute value of -3 is 3. 

If a number is negative, its absolute value will be the positive number with the same magnitude. If a number is positive, it will be its own absolute value. 

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