SOLUTION: Thank you in advance for helping me with writing this problem in interval notation. The absolute value of 2x+1>=3 I have( -infintiy, -2]U[1,infinity ) Am I close?

Algebra ->  Inequalities -> SOLUTION: Thank you in advance for helping me with writing this problem in interval notation. The absolute value of 2x+1>=3 I have( -infintiy, -2]U[1,infinity ) Am I close?       Log On


   

Question 149694This question is from textbook
: Thank you in advance for helping me with writing this problem in interval notation. The absolute value of 2x+1>=3 I have( -infintiy, -2]U[1,infinity ) Am I close? This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%282x%2B1%29%3E=3 Start with the given inequality


Break up the absolute value (remember, if you have abs%28x%29%3E=+a, then x+%3C=+-a or x+%3E=+a)

2x%2B1+%3C=+-3 or 2x%2B1+%3E=+3 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 2x%2B1+%3C=+-3


2x%2B1%3C=-3 Start with the given inequality


2x%3C=-3-1Subtract 1 from both sides


2x%3C=-4 Combine like terms on the right side


x%3C=%28-4%29%2F%282%29 Divide both sides by 2 to isolate x



x%3C=-2 Divide


Now lets focus on the second inequality 2x%2B1+%3E=+3


2x%2B1%3E=3 Start with the given inequality


2x%3E=3-1Subtract 1 from both sides


2x%3E=2 Combine like terms on the right side


x%3E=%282%29%2F%282%29 Divide both sides by 2 to isolate x



x%3E=1 Divide



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Answer:

So our answer is

x+%3C=+-2 or x+%3E=+1



So the solution in interval notation is: (] [)




Here's the graph of the solution set




Note:
There is a closed circle at x=-2 which means that we're including that value from the solution set.


Also, there is a closed circle at x=1 which means that we're including that value from the solution set.