SOLUTION: Solve the conjunction -2 < a + 3 < 8 and graph its solution.

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Question 190006This question is from textbook Structure and Method Book 1
: Solve the conjunction -2 < a + 3 < 8 and graph its solution. This question is from textbook Structure and Method Book 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-2%3Ca%2B3%3C8 Start with the given compound inequality.


-2-3%3Ca%3C8-3 Subtract 3 from all sides.


-5%3Ca%3C8-3 Combine like terms on the left side.


-5%3Ca%3C5 Combine like terms on the right side.


So our answer is -5%3Ca%3C5


So the answer in interval notation is ()


Also, answer in set-builder notation is


Here's the graph of the solution set

Graph of the solution set

Note:
There is an open circle at a=-5 which means that we're excluding this value from the solution set
Also, there is an open circle at a=5 which means that we're excluding this value from the solution set.