SOLUTION: Solve the nonlinear inequality. Express the solution using interval notation. x − 3/x + 1 ≥ 0

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Question 985341: Solve the nonlinear inequality. Express the solution using interval notation.
x − 3/x + 1 ≥ 0
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
x+-+%283%2Fx%29+%2B+1+%3E=+0
%28x%5E2+-3%2Bx%29%2Fx++%3E=+0
x%5E2+%2B+x+-+3+%3E=+0
Now find the zeros for the equality x%5E2+%2B+x+-+3+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-3+=+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=%281%29%5E2-4%2A1%2A-3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+13+%29%29%2F2%5C1+=+1.30277563773199
x%5B2%5D+=+%28-%281%29-sqrt%28+13+%29%29%2F2%5C1+=+-2.30277563773199

Quadratic expression 1x%5E2%2B1x%2B-3 can be factored:
1x%5E2%2B1x%2B-3+=+1%28x-1.30277563773199%29%2A%28x--2.30277563773199%29
Again, the answer is: 1.30277563773199, -2.30277563773199. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-3+%29


Using the graph above, you see that when x is less than or equal to -2.3 or greater than equal t0 1.3 , the equation is satisfied