Arthur D. answered • 12/06/14
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x
x+6
5(x+6)
5(x+6)-28
2[5(x+6)-28]
2[5(x+6)-28]+16
5{2[5(x+6)-28]+16}
5{2[5(x+6)-28]+16}-50
2(5{2[5(x+6)-28]+16}-50)
2(5{2[5x+30-28]+16}-50)
2(5{2[5x+2}+16}-50)
2(5{10x+4+16}-50)
2(5{10x+20}-50)
2(50x+100-50)
2(50x+50)
2*50(x+1)
100(x+1)
100x+100
now do the reverse; subtract 100 and then divide by 100
900-100=800
800/100=8
Arthur D.
tutor
Doing all the operations, as I have shown, simplifies to 100x+100; in other words, doing all the steps, add 6, multiply by 5, etc, etc, is the same as multiplying the number you choose by 100 and then adding 100 to that product.
Jeff chose 8, did all the steps Katie said to do to the number, and ended up with 900. Jeff could have ended up with 900 simply by multiplying the 8 by 100 to get 800 and then adding 100 to 800 to get 900. To get back to Jeff's original number, you do the inverse of "add 100" and "multiply by 100". You subtract 100 and then divide by 100.
If you walk to the store how do you get back home ? You reverse your direction. If you assemble something, to disassemble it, you reverse the steps you took to assemble it. If Jeff chose 9, he would have done all those steps and ended up with 1000. Try it out ! 100*9+100=900+100=1000. 1000-100=900, 900/100=9.
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12/06/14
Arthur D.
tutor
Performing all the steps is the same as multiplying the number by 100 and then adding 100 to the product.
Jeff chose 8. 100*8=800, 800+100=900. Do the inverse to get back to the original number.
900-100=800, 800/100=8 !
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12/07/14
Sarah J.
Oh, okay. I understand now. Thanks so much!
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12/07/14
Arthur D.
tutor
You're very welcome. Sometimes when you post a comment it doesn't get written right away so you post again and all of a sudden both posts are there, that's why you see two posts.
Arthur D.
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12/08/14
Michael W.
I got Arthur's answer, too. The other posted answer must have had an arithmetic oopsie in it somewhere.
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12/09/14
Sarah J.
12/06/14