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Question Number 131075 by benjo_mathlover last updated on 01/Feb/21
If a−3=−b−4=−c−5=d+6=e+7= a−b−c+d+e+8 then a−b−c+d+e =?
$$\mathrm{If}\:\mathrm{a}−\mathrm{3}=−\mathrm{b}−\mathrm{4}=−\mathrm{c}−\mathrm{5}=\mathrm{d}+\mathrm{6}=\mathrm{e}+\mathrm{7}= \\ $$$$\mathrm{a}−\mathrm{b}−\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{8}\:\mathrm{then}\:\mathrm{a}−\mathrm{b}−\mathrm{c}+\mathrm{d}+\mathrm{e}\:=? \\ $$
Answered by EDWIN88 last updated on 01/Feb/21
a =k+3 ; b=−4−k ; c=−k−5 d=k−6 ; e=k−7 ⇔ (k+3)−(−4−k)−(−k−5)+k−6++k−7+8=k ⇔ k+3+4+k+k+5+k−13+8=0 ⇔ 4k=−7 ; k=−(7/4)
$${a}\:={k}+\mathrm{3}\:;\:{b}=−\mathrm{4}−{k}\:;\:{c}=−{k}−\mathrm{5} \\ $$$${d}={k}−\mathrm{6}\:;\:{e}={k}−\mathrm{7} \\ $$$$\Leftrightarrow\:\left({k}+\mathrm{3}\right)−\left(−\mathrm{4}−{k}\right)−\left(−{k}−\mathrm{5}\right)+{k}−\mathrm{6}++{k}−\mathrm{7}+\mathrm{8}={k} \\ $$$$\Leftrightarrow\:{k}+\mathrm{3}+\mathrm{4}+{k}+{k}+\mathrm{5}+{k}−\mathrm{13}+\mathrm{8}=\mathrm{0} \\ $$$$\Leftrightarrow\:\mathrm{4}{k}=−\mathrm{7}\:;\:{k}=−\frac{\mathrm{7}}{\mathrm{4}} \\ $$

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