Question 100436
I'll do the first three, and the absolute value problem, to give you an idea on how to do these



#1

{{{-6>4y}}} Start with the given inequality


{{{-6/4>y}}} Divide both sides by 4



{{{-3/2>y}}} Reduce


So the answer is {{{y<-3/2}}}



<hr>


#2



{{{8-u>4}}} Start with the given inequality



{{{-u>4-8}}}Subtract 8 from both sides



{{{-u>-4}}} Combine like terms on the right side



{{{u<(-4)/(-1)}}} Divide both sides by -1 to isolate u  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{u<4}}} Divide


--------------------------------------------------------------

Answer:

So our answer is {{{u<4}}} 



<hr>


#3




{{{5w>-6w+11}}} Start with the given inequality



{{{5w+6w>11}}} Add 6w to both sides



{{{11w>11}}} Combine like terms on the left side



{{{w>(11)/(11)}}} Divide both sides by 11 to isolate w 




{{{w>1}}} Divide


--------------------------------------------------------------

Answer:

So our answer is {{{w>1}}} 






#4





{{{abs(2h+1)<5}}} Start with the given inequality



Break up the absolute value (remember, if you have {{{abs(x)< a}}}, then {{{x > -a}}} and {{{x < a}}})


{{{2h+1 > -5}}} and {{{2h+1 < 5}}} Break up the absolute value inequality using the given rule



{{{-5 < 2h+1 < 5}}} Combine the two inequalities to get a compound inequality




{{{-6 < 2h < 4}}} Subtract 1 from  all sides



{{{-3 < h < 2}}}  Divide all sides by 2 to isolate h




----------------------------------------------------


Answer:


So our answer is


{{{-3 < h < 2}}}