SOLUTION: Hi tutors: you've been so helpful with this Algebra. here are 2 similar problems that I need help with to solve using the set builder notation 1) 5x-49 is more than/equal to 6-8(

Algebra ->  Inequalities -> SOLUTION: Hi tutors: you've been so helpful with this Algebra. here are 2 similar problems that I need help with to solve using the set builder notation 1) 5x-49 is more than/equal to 6-8(      Log On


   

Question 536564: Hi tutors: you've been so helpful with this Algebra. here are 2 similar problems
that I need help with to solve using the set builder notation
1) 5x-49 is more than/equal to 6-8(2x+7) and
2) -8-11 (3x+7) is less than/equal to 40x-9)
Thanks, and Happy Holidays
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Please post questions one at a time. Thank you.


# 1

5x-49%3E=6-8%282x%2B7%29 Start with the given inequality.


5x-49%3E=6-16x-56 Distribute.


5x-49%3E=-16x-50 Combine like terms on the right side.


5x%3E=-16x-50%2B49 Add 49 to both sides.


5x%2B16x%3E=-50%2B49 Add 16x to both sides.


21x%3E=-50%2B49 Combine like terms on the left side.


21x%3E=-1 Combine like terms on the right side.


x%3E=%28-1%29%2F%2821%29 Divide both sides by 21 to isolate x.


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Answer:

So the solution is x%3E=-1%2F21

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# 2

-8-11%283x%2B7%29%3C=4%28x-9%29 Start with the given inequality.


-8-33x-77%3C=4x-36 Distribute.


-33x-85%3C=4x-36 Combine like terms on the left side.


-33x%3C=4x-36%2B85 Add 85 to both sides.


-33x-4x%3C=-36%2B85 Subtract 4x from both sides.


-37x%3C=-36%2B85 Combine like terms on the left side.


-37x%3C=49 Combine like terms on the right side.


x%3E=%2849%29%2F%28-37%29 Divide both sides by -37 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E=-49%2F37 Reduce.


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Answer:

So the solution is x%3E=-49%2F37


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