SOLUTION: solve and graph 4x-9 less than equal to -8 or x-8 greater than equal to 1

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Question 146781: solve and graph
4x-9 less than equal to -8 or x-8 greater than equal to 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's solve the first inequality 4x-9%3C=-8:


4x-9%3C=-8 Start with the first inequality.


4x%3C=-8%2B9 Add 9 to both sides.


4x%3C=1 Combine like terms on the right side.


x%3C=%281%29%2F%284%29 Divide both sides by 4 to isolate x.


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Now let's solve the second inequality x-8%3E=1:


x-8%3E=1 Start with the second inequality.


x%3E=1%2B8 Add 8 to both sides.


x%3E=9 Combine like terms on the right side.


So our answer is x%3C=1%2F4 or x%3E=9



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


Also, the solution in set notation is:




Here's the graph of the solution set




Note:
There is a closed circle at x=1%2F4 which means that we're including that value from the solution set.


Also, there is a closed circle at x=9 which means that we're including that value from the solution set.