Absolute Value

If we have an unknown or an expression with an unknown within an absolute value, we will ask ourselves which expression will bring us the value of the desired equation, we will divide into cases and discover the unknown.
Example in the equation:  $│x+7│=12$

We will ask ourselves which absolute value expression will be equal to $12$.
The answer will be $12$ or $-12$. (Both an absolute value is equal to $12$ and an absolute $12$ is equal to $-12$).
Therefore, we will take the complete expression and divide it into two cases:
First case:
$x+7=12$
We solve:
$x=5$

Second case:
$X+7=-12$
We solve
$x=-19$

Therefore, the solution to the exercise is: $x=5,-19$

Examples:

• the absolute value of $-7$ is represented as follows: $|7|$;
• the absolute value of $+9$ is represented as follows: $|9|$. 

However, when writing calculations, we will do it as follows:

• $|-20|= 20$
• $|+13.6|=13.6$
• $|(+44)+(-5)|=|+39|=39$
• $|-9+6|=|-3|=3$
• $|-9|+6=9+6=15$
• $|(-56)|+(-13)=56+(-13)=43$
• $28+|4-9|=28+|-5|=28+5=33$

The absolute value of a negative number will always be greater than it. 

The absolute value of a positive number will always be equal to the positive number. 

Examples:

• $|-6|>-6$
• $|+6|=+6$

Fill in the blanks with one of the following symbols: <, >, =. 

• $-4$,$~▯~$,$|-4|$
• $|-9|$,$~▯~$,$+6$
• $|-50|$,$~▯~$,$|+50|$
• $8+5$,$~▯~$,$|-14|$
• $|-5-5|$,$~▯~$,$4+5$
• $|+53|$,$~▯~$,$53$
• $|-3-2|$,$~▯~$,$|6-1|$
• $|14+(-8)|$,$~▯~$,$14+|-8|$
• $14+(-8)$,$~▯~$,$|+14|+(-8)$

Solve the following exercises:

• $|-5+6|=$
• $22-|-53|=$
• $|15-19|+|-9-7|=$
• $|15-19-9|-7=$
• $15-|19-9-7|=$
• $9.7-|4.3+(-6)|=$
• $9.7-4.3+|-6|=$