SOLUTION: I need help solving problems such as 3y -3 < 5y – 4 I start with 3y – 3 < 5y I am never sure if I should subtract 5y from each side or subtract 3y from each side. Then wit

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Question 147109: I need help solving problems such as
3y -3 < 5y – 4
I start with 3y – 3 < 5y
I am never sure if I should subtract 5y from each side or subtract 3y from each side.
Then with 3 < 5y – 4
Do I add four on both sides or subtract 3 from each side?
I will get different answers depending on which way I go.
Can you help?
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3y-3%3C5y-4 Start with the given inequality.


3y%3C5y-4%2B3 Add 3 to both sides.


3y-5y%3C-4%2B3 Subtract 5y from both sides.


-2y%3C-4%2B3 Combine like terms on the left side.


-2y%3C-1 Combine like terms on the right side.


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


y%3E1%2F2 Reduce.


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Answer:

So the answer is y%3E1%2F2


Which approximates to y%3E0.5





So the answer in interval notation is


Also, the answer in set-builder notation is

Here's the graph of the solution set




Note: there is an open circle at y=1%2F2 which means that we're excluding that value from the solution set.