Multistep inequalities

[Lscar92]

negative four times a number plus nine is no more than the number minus twenty one
-4n+9<or=n-21
-9 -9
-4n<or=n-30
-n
-5n<or=-30
div, by -5 this is where i'm confused do i flip the sign since i div. by a neg num?
n<or=6, n>or=6
i am unsure of which is the correct answer

 

[tkhunny]

You do not ever need to be confused. Rather than dividing gy -5, why not add 30 to both sides and then add 5n to both sides? Something magic will happen that will explain multiplication of negatives to you.

 

[Lscar92]

to undo mult. you divide.correct?
so my final answer n>or=6
you confuse me.

 

[tkhunny]

You didn't do what I said. If you would do it, you would stop being confused about me or about negative multiplication.

-5n <= -30

Add 30

-5n + 30 <= 0

Add 5n

30 <= 5n

Divide by 5

6 <= n

Rather than dividing by a negative number and being confused, I entirely avoided the problem with a little algebra so that division was with a positive number. Now you tell me, which way did it come out? Should you switch the inequality or not when dividing by a negative number? Do it both ways and see which gives the correct answer.