SOLUTION: Please help me with this problem Thanks it says solve the following inequal. show a number line as your solution and give the interval notation for the solution 5x-9>2x-7

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Question 145588: Please help me with this problem Thanks it says solve the following inequal. show a number line as your solution and give the interval notation for the solution

5x-9>2x-7


5[3m-(m+4)]<-2(m-4) same directions as the first thanks again!!
Answer by jim_thompson5910(21682) About Me  (Show Source):
You can put this solution on YOUR website!
5x-9%3E2x-7 Start with the given inequality



5x%3E2x-7%2B9Add 9 to both sides


5x-2x%3E-7%2B9 Subtract 2x from both sides


3x%3E-7%2B9 Combine like terms on the left side


3x%3E2 Combine like terms on the right side


x%3E%282%29%2F%283%29 Divide both sides by 3 to isolate x



x%3E2%2F3 Reduce

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Answer:
So our answer is x%3E2%2F3 (which is approximately x%3E0.667 in decimal form)




So the answer in interval notation is


Here's the graph of the solution set

drawing%28500%2C80%2C-8%2C+12%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-8%2C+12%29%2C%0D%0A%0D%0Aarrow%282%2F3%2C0%2C12%2C0%29%2C%0D%0Aarrow%282%2F3%2C0.30%2C12%2C0.30%29%2C%0D%0Aarrow%282%2F3%2C0.15%2C12%2C0.15%29%2C%0D%0Aarrow%282%2F3%2C-0.15%2C12%2C-0.15%29%2C%0D%0Aarrow%282%2F3%2C-0.30%2C12%2C-0.30%29%2C%0D%0A%0D%0Acircle%282%2F3%2C0%2C0.3%29%2C%0D%0Acircle%282%2F3%2C0%2C0.3%29%2C%0D%0Acircle%282%2F3%2C0%2C0.3%29%2C%0D%0Acircle%282%2F3%2C0%2C0.3-0.02%29%0D%0A%29








5%283m-%28m%2B4%29%29%3C-2%28m-4%29+ Start with the given inequality


15m-5%28m%2B4%29%3C-2%28m-4%29+ Distribute




15m-5m-20%3C-2m%2B8 Distribute


10m-20%3C-2m%2B8 Combine like terms on the left side


10m%3C-2m%2B8%2B20Add 20 to both sides


10m%2B2m%3C8%2B20 Add 2m to both sides


12m%3C8%2B20 Combine like terms on the left side


12m%3C28 Combine like terms on the right side


m%3C%2828%29%2F%2812%29 Divide both sides by 12 to isolate m



m%3C7%2F3 Reduce

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Answer:
So our answer is m%3C7%2F3 (which is approximately m%3C2.333 in decimal form)



So the answer in interval notation is




Here's the graph of the solution set

drawing%28500%2C80%2C-3%2C+17%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-3%2C+17%29%2C%0D%0A%0D%0A%0D%0Aarrow%287%2F3%2C0%2C-3%2C0%29%2C%0D%0Aarrow%287%2F3%2C0.30%2C-3%2C0.30%29%2C%0D%0Aarrow%287%2F3%2C0.15%2C-3%2C0.15%29%2C%0D%0Aarrow%287%2F3%2C-0.15%2C-3%2C-0.15%29%2C%0D%0Aarrow%287%2F3%2C-0.30%2C-3%2C-0.30%29%2C%0D%0A%0D%0A%0D%0A%0D%0A%0D%0Acircle%287%2F3%2C0%2C0.3%29%2C%0D%0Acircle%287%2F3%2C0%2C0.3%29%2C%0D%0Acircle%287%2F3%2C0%2C0.3%29%2C%0D%0Acircle%287%2F3%2C0%2C0.3-0.02%29%0D%0A%29