# Solving inequality in Wolfram|Alpha?

Posted 2 months ago
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 Hi everyone, does anyone know why Mathematica does not understand this input? I want to solve this inequality such that I obtain a condition for j.Thank you for the help! Answer
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Posted 2 months ago
 Use Simplify, Collect together all the j, and then push things not containing j across the inequality. Collect[Simplify[j-((β-1)(β^2 j λ+β^2(-j)-β j λ+β j-β^2 j λ q+β^2 j q+β^2 q x z- β^2 q z+β q z-β^2 λ w+β λ w+β^2 λ w x-β^2 x z+β x z+β^2 z-2 β z+z))/ ((β-1)(-β-β^2 λ q+β q+β^2 q x+β^2 λ x-β^2 x+β x+1))]>0,j]/.p1_+p2_>0->p1>-p2 which results in (j*(1+β*(-1+λ+q))*(1+β*(-1+x)))/(1+β*(-1+q+x)+β^2*((-1+q)*x+λ*(-q+x))) > -(((1+β*(-1+x))*(-z+β*(-(λ*w)+z-q*z)))/(1+β*(-1+q+x)+β^2*((-1+q)*x+λ*(-q+x)))) Notice that contains a single j on the left hand side and the left and right hand side denominators are the same and the left and right hand side numerators have a common factor.IF you can justify to yourself that you can multiply and divide both sides without changing the inequality to eliminate those common factors then the condition for j is j(1+β(-1+λ+q)) > -(-z+β(λ w+z-q z)) IF you can further justify one more division without changing the inequality then the condition for j is j > -(-z+β(λ w+z-q z))/(1+β(-1+λ+q)) Please check every step of this very carefully to convince yourself that I have made no mistakes. Answer
Posted 2 months ago
 Thank you very much for your help @Bill Nelson !! Answer