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ExamFever
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Homework Statement
2 - ((x-3)/(x-2)) ≥ ((x-5)/(x-1))
Homework Equations
The Attempt at a Solution
I just want to make sure that certain operations that are allowed with fractions in equations are still valid (or not) in inequalities.
2 - ((x-3)/(x-2)) ≥ ((x-5)/(x-1))
Can I remove the fractions by multiplying by the LCM here?
When I do, I get to the solution:
2(x-2)(x-1) - (x-3)(x-1) ≥ (x-5)(x-2)
this implies
x2-2x +1 ≥ x2-7x+10
-2x+1 ≥ -7x+10
x ≥ 9/5
However, when I put 9/5 into the original inequality I get:
-2 ≥ -4
Of course this is right, however, I was expecting the same values on each side. Is there something wrong with this expectation, or something wrong with my calculation??
Thanks in advance,