SOLUTION: 1. Solve the equation 3x+1/x+1 + 2x-1/x-1=1. 2. Solve the equation 4/c+3 + 5/c+4 = 6/c+7. 3. Solve the equation 0.7x - 0.5x^2 - 0.8 = -6. 4. If x is an integer, solve the inequa

Algebra ->  Equations -> SOLUTION: 1. Solve the equation 3x+1/x+1 + 2x-1/x-1=1. 2. Solve the equation 4/c+3 + 5/c+4 = 6/c+7. 3. Solve the equation 0.7x - 0.5x^2 - 0.8 = -6. 4. If x is an integer, solve the inequa      Log On


   

Question 986003: 1. Solve the equation 3x+1/x+1 + 2x-1/x-1=1.
2. Solve the equation 4/c+3 + 5/c+4 = 6/c+7.
3. Solve the equation 0.7x - 0.5x^2 - 0.8 = -6.
4. If x is an integer, solve the inequality -8 <2x-3《13.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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Limit one problem per post.
Any more, your wasting your time typing.
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0.7x - 0.5x^2 - 0.8 = -6.
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-0.5x%5E2%2B0.7x%2B5.2=0
x%5E2-1.4x-10.4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.5x%5E2%2B0.7x%2B5.2+=+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=%280.7%29%5E2-4%2A-0.5%2A5.2=10.89.

Discriminant d=10.89 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.7%2B-sqrt%28+10.89+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.7%29%2Bsqrt%28+10.89+%29%29%2F2%5C-0.5+=+-2.6
x%5B2%5D+=+%28-%280.7%29-sqrt%28+10.89+%29%29%2F2%5C-0.5+=+4

Quadratic expression -0.5x%5E2%2B0.7x%2B5.2 can be factored:
-0.5x%5E2%2B0.7x%2B5.2+=+-0.5%28x--2.6%29%2A%28x-4%29
Again, the answer is: -2.6, 4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.5%2Ax%5E2%2B0.7%2Ax%2B5.2+%29

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ANSWER: x=-2.6 or x=4