SOLUTION: 3(W + 7) < W – 3 or 4W > W – 6

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Question 174314: 3(W + 7) < W – 3 or 4W > W – 6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's solve the first inequality 3%28w%2B7%29%3Cw-3:


3%28w%2B7%29%3Cw-3 Start with the first inequality.


3w%2B21%3Cw-3 Distribute.


3w%3Cw-3-21 Subtract 21 from both sides.


3w-w%3C-3-21 Subtract w from both sides.


2w%3C-3-21 Combine like terms on the left side.


2w%3C-24 Combine like terms on the right side.


w%3C%28-24%29%2F%282%29 Divide both sides by 2 to isolate w.


w%3C-12 Reduce.


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Now let's solve the second inequality 4w%3Ew-6:


4w%3Ew-6 Start with the second inequality.


4w-w%3E-6 Subtract w from both sides.


3w%3E-6 Combine like terms on the left side.


w%3E%28-6%29%2F%283%29 Divide both sides by 3 to isolate w.


w%3E-2 Reduce.


So our answer is w%3C-12 or w%3E-2




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


Also, the solution in set builder notation is:




Here's the graph of the solution set




Note:
There is an open circle at w=-12 which means that we're excluding that value from the solution set.


Also, there is an open circle at w=-2 which means that we're excluding that value from the solution set.