How do you solve the inequality $1+5/(a-1)<=7/6$ ?

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Answer 1 · 2018-04-11T17:35:19

$color(blue)((-oo,1)uu[31,oo)$

$1+5/(a-1)<=7/6$

Subtract $7/6$ form both sides:

$5/(a-1)-1/6<=0$

Add LHS:

$(30-(a-1))/(6(a-1))<=0$

$(31-a)/(6(a-1))<=0$

Multiply by $6$ :

$(31-a)/(a-1)<=0$

So we need:

$+/-$ and $-/+$

$31-a>=0=>a<=31$

$a-1< 0=>a<1$

$31-a<=0=>a>=31$

$a-1>0=>a>1$

$a<1$ and $a>=31$

$color(blue)((-oo,1)uu[31,oo)$

How do you solve the inequality 1+5/(a-1)<=7/61+5/(a-1)<=7/6?