Question

What are the rules of absolute​

Answer 1

Answer: Look below for 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|=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|

Answer 2

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.

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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