How do you solve the inequality #7/(y+1)>7#?

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Answer 1 · 2016-12-17T14:48:39

The answer is #x in ] -1,0 [#

We rewrite the equation as

#7-7/(y+1)<0#

#(7(y+1)-7)/(y+1)<0#

#(7y+7-7)/(y+1)<0#

#(7y)/(y+1)<0#

Let #f(y)=(7y)/(y+1)#

and #y!=-1#

We do a sign chart

#color(white)(aaaa)##y##color(white)(aaaa)##-oo##color(white)(aaaa)##-1##color(white)(aaaa)##0##color(white)(aaaa)##+oo#

#color(white)(aaaa)##y##color(white)(aaaaaaaa)##-##color(white)(aa)##∥##color(white)(a)##-##color(white)(aa)##+#

#color(white)(aaaa)##y+1##color(white)(aaaa)##-##color(white)(aaa)##∥##color(white)(a)##+##color(white)(aa)##+#

#color(white)(aaaa)##f(y)##color(white)(aaaaa)##+##color(white)(aaa)##∥##color(white)(a)##-##color(white)(aa)##+#

Therefore,

#f(y)<0# when #x in ] -1,0 [#

graph{7x/(x+1) [-41.1, 41.1, -20.55, 20.57]}