SOLUTION: Solve using the addition and multiplication principles. 14x - 8 < -50 The solution is {x|x ? ? } Solve using the addition and multiplication principles. x/6 - 1 < 1/5 (th

Algebra ->  Inequalities -> SOLUTION: Solve using the addition and multiplication principles. 14x - 8 < -50 The solution is {x|x ? ? } Solve using the addition and multiplication principles. x/6 - 1 < 1/5 (th      Log On


   

Question 134097: Solve using the addition and multiplication principles.
14x - 8 < -50
The solution is {x|x ? ? }
Solve using the addition and multiplication principles.
x/6 - 1 < 1/5 (the arrow is underlined)
The solution is {x|x < ?} Simplify your answer.
Please help me..thank you so much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



14x-8%3C-50 Start with the given inequality



14x%2Bcross%28-8%2B8%29%3C-50%2B8 Add 8 to both sides


14x%3C-42 Combine like terms


%281%2Fcross%2814%29%29cross%2814%29x%3C%281%2F14%29%28-42%29 Multiply both sides by 1%2F14 to isolate x



x%3C-3 Multiply and simplify

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Answer:
So our answer is x%3C-3


So the answer in set-builder notation is





# 2



x%2F6-1%3C1%2F5 Start with the given inequality



%2830%29%28x%2Fcross%286%29-1%29%3C%2830%29%281%2Fcross%285%29%29 Multiply both sides by the LCM of 30. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



5x-30%3C6 Distribute and multiply the LCM to each side



5x%2Bcross%28-30%2B30%29%3C6%2B30Add 30 to both sides


5x%3C36 Combine like terms


%281%2Fcross%285%29%29cross%285%29x%3C%281%2F5%2936 Multiply both sides by 1%2F5 to isolate x



x%3C36%2F5 Multiply

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Answer:
So our answer is x%3C36%2F5 (which is approximately x%3C7.2 in decimal form)


So the answer in set-builder notation is or (which is in decimal form)