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

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:

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 =)

  • Pre-Algebra -

    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 ?

  • Pre-Algebra -

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

  • Pre-Algebra -

    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 .

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