Can someone please show me how to solve these problems step-by-step so that I can understand how to do them?

Question

1.Use inverse operations to write a related inequality and solve for the variable:
d/6 < 12

2.Use inverse operations to solve the inequality:
m-27=85

3.Use transformations to solve the equation:
2.5 (6+k)=3k

4.Use transformations to solve the inequality:
19-3m+5+7m < 0

Basically I don't get transformations and inverse operations. Pleeasee help! THANKS A MILLION =)
-MC

Answer 1

remember the inverse operation of multiplication is division and vice versa
and the inverse operation of addition is subtraction and vice versa

so in #1 ,
d/6 < 12 , we have a division by 6, so the inverse is multiplication by 6

so multiply both sides by 6
d < 72

in #2
m-27 = 85
m - 27 + 27 = 85 + + 27
m = 112

looks like a big deal is made about nothing

using "transformations" to solve such trivial questions as #3 and #4 ????
Why not just go ahead and solve it ?

Answer 2

Ummm OK thanks; I think I have a couple more questions coming up...
-MC

Answer 3

Josh is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.

Company A charges and allows unlimited mileage.
Company B has an initial fee of and charges an additional for every mile driven.
For what mileages will Company A charge less than Company B?
Use for the number of miles driven, and solve your inequality for .