SOLUTION: How do you solve and graph an inequalitie like x - 2 > 2x + 1 or -10 > -2x - 2?

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Question 151741: How do you solve and graph an inequalitie like x - 2 > 2x + 1 or -10 > -2x - 2?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's solve the first inequality x-2%3E2x%2B1:


x-2%3E2x%2B1 Start with the first inequality.


x%3E2x%2B1%2B2 Add 2 to both sides.


x-2x%3E1%2B2 Subtract 2x from both sides.


-x%3E1%2B2 Combine like terms on the left side.


-x%3E3 Combine like terms on the right side.


x%3C%283%29%2F%28-1%29 Divide both sides by -1 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3C-3 Reduce.


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Now let's solve the second inequality -10%3E-2x-2:


-10%3E-2x-2 Start with the second inequality.


0%3E-2x-2%2B10 Add 10 to both sides.


2x%3E-2%2B10 Add 2x to both sides.


2x%3E8 Combine like terms on the right side.


x%3E%288%29%2F%282%29 Divide both sides by 2 to isolate x.


x%3E4 Reduce.


So our answer is x%3C-3 or x%3E4


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


So the solution in set notation is:




Here's the graph of the solution set




Note:
There is an open circle at x=-3 which means that we're excluding that value from the solution set.


Also, there is an open circle at x=4 which means that we're excluding that value from the solution set.