SOLUTION: I am working on Solving Compound Inequalities The problem I'm working on is as follows: Solve the compound inequality, if possible. Graph the solution set (if one exists) and wr

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Question 348550: I am working on Solving Compound Inequalities
The problem I'm working on is as follows:
Solve the compound inequality, if possible. Graph the solution set (if one exists) and write it using interval notation:
-4%28x%2B2%29%3C=12 or 3x%2B8%3C11
I've solved both linear equations and have what follows:
x%3C=-9%2F2 or x%3C1
My problem is the interval notation. I graphed the answers & I don't understand why the answer in the back of the book is (-infinity, 1).
They intersect at -9/2. I thought the answer would be no solution.
The only thing I can think of, is that if the answer intersects and goes both ways, the answer is (-infinity, infinity), but since this one is only going negative, it's (-infinity, 1).
Thank you for your time!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm assuming that the first inequality should be -4%28x%2B2%29%3E=12 and the solution to that inequality is x%3C=-5


Since x can be either less than or equal to -5 or less than 1, this means that the solution set is really just x%3C1 (since -5 is less than 1). We can completely ignore x%3C=-5 as this entire solution set lies within x%3C1


So the solution to -4%28x%2B2%29%3E=12 or 3x%2B8%3C11 is x%3C1 and it is represented in interval notation by


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim