SOLUTION: How do you solve: 5/9w + 8/9 = 3w This is our first time dealing with fractions in Algebra and we are stuck.

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Question 402500: How do you solve: 5/9w + 8/9 = 3w
This is our first time dealing with fractions in Algebra and we are stuck.
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5/9w + 8/9 = 3w
Multiply thru by 9w
5 + 8w = 27w^2
27w%5E2+-+8w+-+5+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 27x%5E2%2B-8x%2B-5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-8%29%5E2-4%2A27%2A-5=604.

Discriminant d=604 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+604+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+604+%29%29%2F2%5C27+=+0.603266878794241
x%5B2%5D+=+%28-%28-8%29-sqrt%28+604+%29%29%2F2%5C27+=+-0.306970582497945

Quadratic expression 27x%5E2%2B-8x%2B-5 can be factored:
27x%5E2%2B-8x%2B-5+=+%28x-0.603266878794241%29%2A%28x--0.306970582497945%29
Again, the answer is: 0.603266878794241, -0.306970582497945. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+27%2Ax%5E2%2B-8%2Ax%2B-5+%29

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w = (4 ± sqrt(151))/27
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After doing that, it occured to me you might mean (5/9)w, not 5/(9w)
In that case:
5/9w + 8/9 = 3w
Multiply thru by 9 to eliminate fractions
5w + 8 = 27w
8 = 22w
22w = 8
w = 8/22
w = 4/11
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Use parentheses, they're free.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F9w+%2B+8%2F9+=+3w+.........first, find common denominator for left side; for 9w and 9 it is 9w...multiply both sides by 9w

9w%285%2F9w%29+%2B+9w%288%2F9%29+=+3w%2A9w+

cross%289w%29%285%2Fcross%289w%29%29+%2B+cross%289%29w%288%2Fcross%289%29%29+=+27w%5E2+

5%2B+8w+=+27w%5E2+

27w%5E2+-8w+-+5+=+0.......use quadratic formula to solve for w

w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

w+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%2A27%2A%28-5%29+%29%29%2F%282%2A27%29+

w+=+%288+%2B-+sqrt%28+64+-108%2A%28-5%29+%29%29%2F%2854%29+

w+=+%288+%2B-+sqrt%28+64+%2B+540+%29%29%2F%2854%29+

w+=+%288+%2B-+sqrt%28+604%29%29%2F%2854%29+

w+=+%288+%2B-+%28+24.6%29%29%2F%2854%29+

first solution:

w1+=+%288+%2B+%28+24.6%29%29%2F%2854%29+
w1+=+%28+32.6%29%2F54+
w1+=++0.6+

second solution:
w2+=+%288+-+%28+24.6%29%29%2F%2854%29+

w2+=+%28+-16.6%29%2F54+

w2+=+-+0.3+

check: if w1+=++0.6+

5%2F9w+%2B+8%2F9+=+3w+

5%2F%289%280.6%29%29+%2B+8%2F9+=+3%280.6%29+

5%2F%285.4%29+%2B0.9+=+1.8+

0.9+%2B+0.9+=+1.8+

1.8+=+1.8+