Annette Arroyo

2020-12-24

Simplifying Absolute Value Express the quantity without using absolute value.

timbalemX

Given:
A value is lower than B value.
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.

user_27qwe

To simplify the expression $a+b+|a-b|$, where $a, without using absolute value, we can consider two equation: when $a-b$ is positive and when $a-b$ is negative.
Equation 1: $a-b>0$
In this equation, $|a-b|=a-b$. Substituting this into the expression, we have:
$a+b+|a-b|=a+b+\left(a-b\right).$
Now we can simplify by combining like terms:
$a+b+|a-b|=a+b+a-b.$
Rearranging the terms:
$a+b+|a-b|=2a.$
Therefore, when $a-b>0$, the expression simplifies to $2a$.
Equation 2: $a-b<0$
In this equation, $|a-b|=-\left(a-b\right)$. Substituting this into the expression, we have:
$a+b+|a-b|=a+b-\left(a-b\right).$
Simplifying by combining like terms:
$a+b+|a-b|=a+b-a+b.$
Rearranging the terms:
$a+b+|a-b|=2b.$
Therefore, when $a-b<0$, the expression simplifies to $2b$.

Jazz Frenia

Explanation:
To express the quantity $a+b+|a-b|$ without using absolute value, we need to consider two cases: when $a-b$ is positive and when $a-b$ is negative.
Case 1: $a-b>0$
In this case, $|a-b|=a-b$, so the expression becomes $a+b+\left(a-b\right)$. We can simplify this further:
$a+b+\left(a-b\right)=a+b+a-b=2a$
Case 2: $a-b<0$
When $a-b$ is negative, $|a-b|=-\left(a-b\right)$. Therefore, the expression becomes $a+b-\left(a-b\right)$. Simplifying this, we have:
$a+b-\left(a-b\right)=a+b-a+b=2b$
Therefore, the simplified expression, without using absolute value, is:

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