SOLUTION: im having a problem on how to solve this one. i've tried to do it several times but i think whats confusing me is the negative in front of the absoulte value. if you could help me

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Question 1094125: im having a problem on how to solve this one. i've tried to do it several times but i think whats confusing me is the negative in front of the absoulte value. if you could help me with this one problem id really appericate it
-11 less than or equal to 5-/2p+4/
* the / infront of 2p+4 means absolute value
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

There are many types of equations or inequalities where a negative in front of an expression can be confusing, or make solving more difficult. A basic thing to do in such cases, if possible, is to move the confusing expression to the other side of the equation or inequality so it no longer has the negative sign. For your example...






I will assume you can solve it from there....
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
-11 <= 5 - |2p+4|  ====>

|2p+4| <= 5 + 11  ====>

|2p+4| <= 16  ====>  (divide both side by 2. You will get an equivalent inequality)  ====>  

|p+2| <= 8  ====>


The solution set are those p in a number line that are remoted not farther than 8 units from -2.


So, the solution set is  -2 -8 <= p <= -2 +8,   or, which is the same,

-10 <= p <= 6.


Answer.  The solution set is the segment [-10,6].

When you got the inequality of the type |p+2| <= 8, it is not necessary to continue analytic solution.

You can get the answer quicker if you KNOW what the absolute value means GEOMETRICALLY.



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