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Question Number 44502 by Tip Top last updated on 30/Sep/18

$$\mathrm{If}\mathrm{a}>\mathrm{b},\mathrm{and}\mathrm{c}>\mathrm{d},\mathrm{prove}\mathrm{that}\mathrm{a}-\mathrm{c}\mathrm{may}\mathrm{be}\mathrm{greater}\mathrm{than},$$ $$\mathrm{equal}\mathrm{to}\mathrm{or}\mathrm{less}\mathrm{than}\mathrm{b}-\mathrm{d}.$$ $$$$

Answered by MrW3 last updated on 30/Sep/18

$$a=b+\delta ,\delta >0$$ $$c=d+\varrho ,\varrho >0$$ $$a-c=(b-d)+(\delta -\varrho )$$ $$(a-c)-(b-d)=(\delta -\varrho )$$ $$$$ $$if\delta >\varrho ,(a-c)-(b-d)>0$$ $$\Rightarrow a-cisgreaterthanb-d$$ $$$$ $$if\delta =\varrho ,(a-c)-(b-d)=0$$ $$\Rightarrow a-cisequaltob-d$$ $$$$ $$if\delta <\varrho ,(a-c)-(b-d)<0$$ $$\Rightarrow a-cislessthanb-d$$

Commented byTip Top last updated on 30/Sep/18

$$$$ $$$$ $$\mathrm{Thank}\mathrm{you}\mathrm{Sir}$$

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