EVALUATING ABSOLUTE VALUE EXPRESSIONS

What is absolute value ?

Absolute value means “ Distance away from zero “ on a number line.

Distance is always positive or zero

Its denoted by |x|. (where x is any integer)

For example :

1. If x = 5,

|5| = 5, it is 5 units away from 0

2. If x = -5,

|-5| = 5, it is 5 units away from 0

Evaluate the following absolute functions for x = 4.

Example 1 :

|x + 6|

Solution :

= |x + 6|

Substitute x = -4.

= |-4 + 6| 

= |2|

= 2

Example 2 :

|x - 6|

Solution :

= |x - 6|

Substitute x = -4.

= |-4 - 6| 

= |-10|

= 10

Example 3 :

|2x + 3|

Solution :

= |2x + 3|

Substitute x = -4.

= |2(-4) + 3| 

= |-8 + 3|

= |-5|

= 5

Example 4 :

|7 - x|

Solution :

= |7 - x|

Substitute x = -4.

= |7 – (-4)| 

= |7 + 4|

= |11|

= 11

Example 5 :

|x - 7|

Solution :

= |x - 7|

Substitute x = -4.

= |-4 – 7| 

= |-11|

= 11

Example 6 :

|x² – 6x|

Solution :

= |x² – 6x|

Substitute x = -4.

= |(-4)² – 6(-4)| 

= |16 + 24|

= |40|

= 40

Example 7 :

|6x – x²|

Solution :

= |6x – x²|

Substitute x = -4.

= |6(-4) – (-4)²| 

= |-24 - 16|

= |-40|

= 40

Example 8 :

|x|/(x + 2)

Solution :

= |x|/(x + 2)

Substitute x = -4.

= |-4|/(-4 + 2)

= 4/(-2)

= -2

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