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# Basic Math/Algebra Absolute Value

Question
I failed algebra last year and now I'm doing an online class.
I forgot how to do these:

8 = |5y+2|

1>|2-0.8n|

|0.25y+1| = 0.5

You treat what is in the absolute value bracket as a negative and a positive and solve for both.  So, pretend that the brackets are parens and put a - in front of one and + in front of the other.

8 = |5y+2| would be
8 = +(5y+2) and 8 = -(5y+2) which equals
8 = 5y+2 and 8 = -5y-2  now solve both for y
6=5y  and 10 = -5y
y = 6/5 and y = -2

1>|2-0.8n|  to solve inequalities, you change the greater or less than sign to =
1=(2-8/10n)  1= -(2-8/10n)
1=2-8/10n  1= -2+8/10n
-1 = -8/10n    3 = 8/10n
n = 10/8     n = 30/8

Inequalities take an extra step, now you need to determine if the answer is between the 2 solutions or less than and greater than.  Pick a number between the two and see if the solution is true

1>|2- 8/10(9/8)|
1>|2 - 72/80|  False, so try a number greater than 10/8, but less then 30/8
1>|2- 8/10(11/8)|
1>|2- 88/80|  True statement, so n > 10/8 and less than 30/8, written as 10/8 < n < 30/8

You can check your work by substituting a number greater than 30/8 to confirm that n is between the two.

I'll leave the last one for you to practice on.

Basic Math

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#### Lynn Houston

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