# EVALUATE ABSOLUTE VALUE EXPRESSIONS

## About "Evaluate absolute value expressions"

Evaluate absolute value expressions :

To evaluate absolute value expressions, first we have to apply the given value instead of the given variable in the question.

The absolute value of a number is the number’s distance from 0 on a number line.

In case we have negative values inside the sign modulus, we have to consider it as positive value.

Let us see some example problems.

Example 1 :

Evaluate the following absolute value expression

|x + 6| - 4 for x = -3

Solution :

|x + 6| - 4 for x = -3

In order to evaluate the given absolute value expression, we have to apply the value -3 instead of the variable x.

=  |-3 + 6| - 4

=  |3| - 4

=  3 - 4 = -1

Hence the answer is -1

Example 2 :

Evaluate the following absolute value expression

|-8 - x| + 3 for x = -1

Solution :

|-8 - x| + 3 for x = -1

In order to evaluate the given absolute value expression, we have to apply the value -1 instead of the variable x.

=  |-8 - (-1)| + 3

=  |-8 + 1| + 3

=  |-7| + 3

=  7 + 3

=  10

Hence the answer is 10

Example 3 :

Evaluate the following absolute value expression

8 + |8 - x| + |x - 2| for x = 0

Solution :

8 + |8 - x| + |x - 2|

In order to evaluate the given absolute value expression, we have to apply the value 0 instead of the variable x.

=  8 + |8 - 0| + |0 - 2|

=  8 + |8| + |- 2|

=  8 + 8 + 2

=  18

Hence the answer is 18.

Example 4 :

Evaluate the following absolute value expression

7 + |3 - 2x| + |5x - 7| for x = -3

Solution :

7 + |3 - 2x| + |5x - 7|

In order to evaluate the given absolute value expression, we have to apply the value -3 instead of the variable x.

=  7 + |3 - 2(-3)| + |5(-3) - 7|

=  7 + |3 + 6| + |-15 - 7|

=  7 + |9| + |-22|

=  7 + 9 + 22

=  38

Hence the answer is 38.

Example 5 :

Evaluate the following absolute value expression

-x + |7 - 4x| + |2x - 1| for x = -2

Solution :

-x + |7 - 4x| + |2x - 1|

In order to evaluate the given absolute value expression, we have to apply the value -2 instead of the variable x.

=  -(-2) + |7 - 4(-2)| + |2(-2) - 1|

=  2 + |7 + 8| + |-4 - 1|

=  2 + |15| + |-5|

=  2 + 15 + 5

=  22

Hence the answer is 22.

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