SOLUTION: Hello out there,I need some help with some tough problems,the first one is,Solve:x/5=x+4/9.The next one is,Solve:1/2x+1/x=3/8.The third one is,Solve:3y/2=7+y/4.And the last one is,

Algebra ->  Equations -> SOLUTION: Hello out there,I need some help with some tough problems,the first one is,Solve:x/5=x+4/9.The next one is,Solve:1/2x+1/x=3/8.The third one is,Solve:3y/2=7+y/4.And the last one is,      Log On


   

Question 115699: Hello out there,I need some help with some tough problems,the first one is,Solve:x/5=x+4/9.The next one is,Solve:1/2x+1/x=3/8.The third one is,Solve:3y/2=7+y/4.And the last one is,Simplify:5/3x+2/x,thanks to whoever can help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F5=x%2B4%2F9 Start with the given equation



%2845%29%28x%2F5%29=%2845%29%28x%2B4%2F9%29 Multiply both sides by the LCM of 45. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



9x=45x%2B20 Distribute and multiply the LCM to each side



9x-45x=20 Subtract 45x from both sides


-36x=20 Combine like terms on the left side


x=%2820%29%2F%28-36%29 Divide both sides by -36 to isolate x



x=-5%2F9 Reduce

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Answer:
So our answer is x=-5%2F9 (which is approximately x=-0.555555555555556 in decimal form)

1%2F%282x%29%2B1%2F%28x%29=3%2F8 Start with the given expression



Now multiply both sides by the LCD 8x to eliminate every fraction

%288x%29%281%2F%282x%29%2B1%2F%28x%29%29=%288x%29%283%2F8%29


4%2B8=3x


12=3x Combine like terms on the left side


0=3x-12Subtract 12 from both sides


-3x=-12 Subtract 3x from both sides


x=%28-12%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=4 Divide

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Answer:
So our answer is x=4






3y%2F2=7%2B1y%2F4 Start with the given equation



%284%29%283y%2F2%29=%284%29%287%2B1y%2F4%29 Multiply both sides by the LCM of 4. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



6y=28%2B1y Distribute and multiply the LCM to each side



6y=28%2By Combine like terms on the right side


6y-y=28 Subtract y from both sides


5y=28 Combine like terms on the left side


y=%2828%29%2F%285%29 Divide both sides by 5 to isolate y



y=28%2F5 Reduce

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Answer:
So our answer is y=28%2F5 (which is approximately y=5.6 in decimal form)





5%2F3x%2B2%2Fx Start with the given expression


5%2F3x%2B%283%2F3%29%282%2Fx%29 Multiply the 2nd term by 3%2F3


5%2F%283x%29%2B6%2F%283x%29 Multiply


11%2F%283x%29 Add the fractions