SOLUTION: 1/3x=3x-9 i am a grandmother trying to help my grandchild. Although I aced algebra in high school, that was over half century ago. i having been trying for days with the help

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Question 404423: 1/3x=3x-9
i am a grandmother trying to help my grandchild. Although I aced algebra in high school, that was over half century ago. i having been trying for days with the help of the internet and textbooks and just can't figure out how to do this simple math. maybe you can help. please show steps.
Found 2 solutions by ankor@dixie-net.com, MathLover1:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F3x = 3x - 9
Multiply both sides by 3 to get rid of the denominators
1x = 9x - 27
+27 = 9x - x
27 = 8x
x = 27%2F8
x = 33%2F8 or 3.375
:
:
Check solution in original problem
1%2F3*27%2F8 = 3x - 9
cancel 3 into 27
9%2F8 = 3*27%2F8 -9
9%2F8 = 81%2F8 - 9
9%2F8 = 81%2F8 - 72%2F8; confirms our solution

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F3x%29=3x-9...first, get a rid of denominator, multiply equation by 3x

3x%281%2F3x%29=3x%2A3x-9%2A3x

cross%283x%29%281%2Fcross%283x%29%29=+9x%5E2-+27x

1+=+9x%5E2-+27x.......add -1 to both sides
1-1+=+9x%5E2-+27x+-1

0+=+9x%5E2-+27x+-1
or

9x%5E2-+27x+-1+=+0......use quadratic formula to find roots
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
you have: a=9, b=+-27 and c=+-1.....plug it in quadratic formula


x+=+%28-%28-27%29+%2B-+sqrt%28+%28-27%29%5E2-4%2A9%2A%28-1%29+%29%29%2F2%2A9+


x+=+%2827+%2B-+sqrt%28+%28729+%2B+36+%29%29%29%2F18+


x+=+%2827+%2B-+sqrt%28+765%29%29%2F18+


x+=+%2827+%2B-+27.66%29%2F18+

x1+=+%2827+%2B+27.66%29%2F18+

x1+=+%2854.66%29%2F18+

x1+=+3.037+.........first root


x2+=+%2827+-+27.66%29%2F18+

x2+=+%28-0.66%29%2F18+

x2+=+-0.037+.........second root


check:

%281%2F3x%29=3x-9.....plug in x1+=+3.037+

%281%2F3%2A3.037%29=3%2A3.037-9

%281%2F9.11%29=+9.11-9

%280.11%29=+0.11