What are the all rules of absolute

Look below.

Step-by-step explanation:

1.  |–a| = |a|

2.  |a| ≥ 0

3.  Products: |ab| = |a||b|

4.  Quotients: |a / b| = |a| / |b|

5.  Powers: |an| = |a|n

6.  Triangle Inequality:

        |a + b| ≤ |a| + |b|

7.  Alternate Triangle Inequality:

        |a – b| ≥ |a| – |b|

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Look below for full explanation...

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|=a2Rules:1.  |–a| = |a|2.  |a| ≥ 0 3.  

RULES:

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|  

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

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