# Simplifying Absolute Value Express the quantity without using absolute value.a+b+|a-b|,where a<b

Annette Arroyo 2020-12-24 Answered

Simplifying Absolute Value Express the quantity without using absolute value.

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Given:
The value of a is less than value of b.
Calculation:
The absolute value of a real number x is,

The value of a is less than b, so the subtraction will result in a negative value.
$|a-b|=-\left(a-b\right)=b-a$ (1)
Use the value of $|a-b|$ from equation (1), the quantiny $a+b+|a-b|$ is,
$a+b+|a-b|=a+b+b-a=2b$
The quantity $a+b+|a-b|$ without using the absolute value is 2b.