What are the rules of absolute

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

Step-by-step explanation:

An absolute value equation in the form |ax+b|=c | a x + b | = c has the following properties: If c<0,|ax+b|=c has no solution. If c=0,|ax+b|=c has one solution. If c>0,|ax+b|=c has two solutions.

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Step-by-step explanation:  Algebra rules for absolute values are listed below. 
Piecewise Definition:|a|={aifa≥0−aifa<0|a|={aifa≥0−aifa<0

Square root definition:|a|=√a2|a|=a2

Rules:

1. |–a| = |a|2.  |a| ≥ 0 3.  

Products: |ab| = |a||b| 4.  

Quotients: |a / b| = |a| / |b| 5.  

Powers: |an| = |a|n6.  

Triangle Inequality:         |a + b| ≤ |a| + |b| 7.  

Alternate Triangle Inequality:         |a – b| ≥ |a| – |b| 

PLEASE BE CAREFUL!!    Sums:   |a + b| is not the same as |a| + |b|                                                  Differences:   |a – b| is not the same as |a| – |b|  

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068