This week in Pre-calculus 11 I learned about the absolute values of real numbers and how to solve for them. I learned that the absolute value of a real number is defined as the principal square root of the square of a number.

Principle square root:

The symbol used for the absolute value of a number is two vertical lines: |   |

When solving for the absolute value of a number you are saying how far it is away from zero. Whenever you are trying to find the absolute value of a negative number the value will always be positive because, you cant have a negative distance.

ex.

• |6| = 6 (6 is 6 numbers away from 0)
• |-12| = 12 (-12 is 12 numbers away from 0)
• |45| = 45 (45 is 45 numbers away from 0)

If there is an equation inside the absolute value symbol you must solve the equation and find the absolute value of the product.

ex.

• |1 – 5| = |-4| = 4
• |4 + 6| = |10| = 10
• |3 – 9(-2)|= |3 + 18| = |21| = 21

If there is a coefficient in front of the absolute value symbol then you have to first solve for the absolute value and then multiply it by the coefficient. You do not distribute the coefficient inside the symbols.

ex.

• 5 |2 + 4(-3)|
• 5 |2 – 12|
• 5 |-10|
• 5(10)
• 50

ex.

• – |-|
• – |-8|
• -(8)
• -8