Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Algebra - Absolute values - the concept.
Test Yourself 1.


 

Statement: Interpretation  
1. x < |4|

1. Values have to less than the numeric value of 4 on either side of the origin. Hence the values for x are restricted to the range from x = -4 to x = +4.

  
2. |a| > 10

2. Values for x are restricted to the range
below a = -10 and above a = +10.

  
3. 2 < |s| < 5

3. Rewrite the inequality without the absolute value:

2 < s < 5 shows that values for s are between 2 and 5.

2 < -s < 5 is rewritten as -2 > s > -5 or -5 < s < -2.

This shows that values for s are also between -5 and -2.

  
4. |z| < -1 4. The absolute value sign indicates values for z have to be positive. So there is no possibility that z can be less than -1. Hence it is a nonsense statement.  

5. How much money do you have?

|-$5| = $5

But you still owe someone $5.