SOLUTION: solve for x. 2x+5/2>3/2x-2

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: solve for x. 2x+5/2>3/2x-2      Log On


   

Question 266466: solve for x. 2x+5/2>3/2x-2
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
I hope i understood your ? correctly...if not make sure you put parenthisies around your fractions, so us tutors know what your talking about.
%282x%29%2B%285%2F2%29%3E%283%2F2x%29-2
%282x%29%282x%29%2B%285%2F2%29%282x%29%3E%283%2F2x%29%282x%29-2%282x%29
%284x%5E2%29%2B%285x%29%3E%283%29-4x
%284x%5E2%29%2B%285x%29%2B4x-3%3E%283%29-4x%2B4x-3
4x%5E2%2B9x-3%3E0
u will need to use the quadratic formula. but remember that this is an inequality.
x%3E0.294727086450068
x%3C-2.54472708645007
Please remember to check your answers to place the correct symbols
***The graph is incorrect as i dont know a solver for inequality equations
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B9x%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=%289%29%5E2-4%2A4%2A-3=129.

Discriminant d=129 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+129+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+129+%29%29%2F2%5C4+=+0.294727086450068
x%5B2%5D+=+%28-%289%29-sqrt%28+129+%29%29%2F2%5C4+=+-2.54472708645007

Quadratic expression 4x%5E2%2B9x%2B-3 can be factored:
4x%5E2%2B9x%2B-3+=+4%28x-0.294727086450068%29%2A%28x--2.54472708645007%29
Again, the answer is: 0.294727086450068, -2.54472708645007. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B9%2Ax%2B-3+%29