Expert: Lynn Houston - 7/28/2010

Question
8 = |  5 y + 2 |

 1 - 0.5 p |  ≤ 2


2 t - 3 | + 2 = 5

| 3 k - 2 | < 4

this is some of the basics i need help with to help me out with so i can learn to the rest

Answer
Here's a website that explains absolute values better than I could, but basically, you value between the bars can be positive and negative.  So, to solve the first one, you remove the bars and solve for 5y+2 = 8, then solve again for 5y+2 = -8.  So
5y = 6 and 5y = -10
y = 6/5 and y = -2

For the inequalities, you again for solve the positive and negative values.

|1- .5p| ≤ 2 would be

-2 ≤ |1- .5p| ≤ 2, which you just solve in 2 parts

-2 ≤ 1- .5p and 1- .5p ≤ 2

For this last type, you first move anything that is not within the absolute value to the other side of the eq


|2 t - 3 | + 2 = 5   subtract 2 from both sides of the equation

|2 t - 3 |  = 3 then solve the same as the first one.