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)#