Due to math content, this page has special requirements (including JavaScript) for full functionality.
With your current viewing scenario, it is not appearing and behaving as it is supposed to!
Please visit Dr. Carol J.V. Fisher's Homepage (link at left) to learn what this site has to offer.
Watch the "Welcome" video to get started—hope to see you back here soon!
Dr. Carol J.V. Fisher's Homepage
SOLVING SIMPLE ABSOLUTE VALUE SENTENCES
Jump right to the exercises!
The concepts for this exercise are summarized below.
For a complete discussion, read the text.
Recall that |x| gives the distance between x and 0 .
If you think in terms of distance, then it's easy to solve sentences involving absolute value!
EXAMPLES:
Solve: |x| = 3
Solution: We want all numbers x whose distance from zero is 3.
Remember that you can "walk" from zero in two directions: to the right, and to the left.
Answer: x = 3 or x = -3
Solve: |x| < 3
Solution: We want all numbers x whose distance from zero is less than 3.
Thus, you can walk less than three units to the right, or less than three units to the left.
You end up with all the numbers between -3 and 3:
Answer: -3 < x < 3
Solve: |x| > 3
Solution: We want all numbers x whose distance from zero is more than 3.
Thus, you can walk more than three units to the right, or more than three units to the left.
You end up with the two "pieces" shown below:
Answer: x > 3 or x < -3
Solve: |x| < -1
Solution: there are no solutions (distance can't be negative)
Solve: |x| > -1
Solution: all real numbers are solutions (all distances are nonnegative)
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.