SOLUTION: hi I am stuck on this problem I will give you the problem then show you what I did so you can tell me where I made my mistakes. Thanks {{{(z+7/9)+1=((2z+1)/6)/18}}} I did this..

Algebra ->  Linear-equations -> SOLUTION: hi I am stuck on this problem I will give you the problem then show you what I did so you can tell me where I made my mistakes. Thanks {{{(z+7/9)+1=((2z+1)/6)/18}}} I did this..      Log On


   

Question 71905: hi I am stuck on this problem I will give you the problem then show you what I did so you can tell me where I made my mistakes. Thanks %28z%2B7%2F9%29%2B1=%28%282z%2B1%29%2F6%29%2F18
I did this...%28z%2B7%2F9%2B1%29%2A18=2z%2B1%2F6%2F18%2A18
18z%2B126%2F9%2B18=2z%2B1%2F6
2z%2B14%2B18=2z%2B1%2F6%2A6
12z%2B192-1=2z%2B1-1
12z%2B191=2z
12z-12z%2B191=2z-12z
191=-10z
z=-19.1
Looking forward to hearing from you.
Found 3 solutions by bucky, jim_thompson5910, ankor@dixie-net.com:
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
(z+7/9)+1={(2z+1)/6}/18
I did this...
z+7/9+1*18=2z+1/6/18*18 <--- OK
18z+126/9+18=2z+1/6 <---- OK
2z+14+18=2z+1/6*6
.
The previous step seems to be in error. One error is that you show multiplying by 6 on
one side only. But it appears that this was a typo only, and in the next step below it
appears as if you did also multiply the left side by 6. However, a significant error
seems to be that on the left side in the line I marked OK, you had 18z on the left side
and in the very next line it shows as 2z. What happened to the missing 16z?
.
12z+192-1=2z+1-1 <--- OK except the 12z should be 18z*6 = 108z
12z+191=2z
12z-12z+191=2z-12z
191=-10z <--- the right side here should be -106z
.
z=-19.1 <--- weird as is seems, the correct answer to this problem is -191/106
.
You appear to have your act together about how to do problems like this. Just that one
little mistake got you off track. Good going .... keep it up ...

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
On the second step, where you multiplied everything by 18, the left side looks good, but the right side does not. The reason you multiplied everything by 18 was to cancel out the 18 in the denominator, and it should have stopped there. Here's what it should look like
%28z%2B7%2F9%29%2B1=%28%282z%2B1%29%2F6%29%2F18 Start with given problem
18%28%28z%2B7%2F9%29%2B1%29=cross%2818%29%2A%28%28%282z%2B1%29%2F6%29%2Fcross%2818%29%29The 18's on the right cancel, you dont have to worry about those anymore.
18z%2B126%2F9%2B18+=+%282z%2B1%29%2F6 Now just solve for z
6%2818z%2B14%2B18%29+=+cross%286%29%2A%28%282z%2B1%29%2Fcross%286%29%29
108z%2B84%2B108+=+2z%2B1 Get all z's to one side and everything else to the opposite side
108z-2z+=+1-108-84
106z+=+-191
z+=+-191%2F106
z+=+-1.801887approximately
Check:
%28-1.801887%2B7%2F9%29%2B1+=+%28%282%28-1.801887%29%2B1%29%2F6%29%2F18
-1.02411%2B1+=+%28-3.603774+%2B+1%29%2F6%2A18
-0.02411+=+-0.02411+ This shows that this answer works
You can also graph (z+7/9)+1=((2z+1)/6)/18 by changing z to x and graphing them individually (ie y=(x+7/9)+1) and their intersection should be (-1.801887,-0.02411) which is the result we got.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28z%2B7%2F9%29%2B+1 = %28%282z%2B1%29%2F6%29%2F18
:
%28z%2B7%2F9%2B1%29%2A18=2z%2B1%2F6%2F18%2A18
Right here you should have
18z%2B126%2F9%2B18=%282z%2B1%29%2F6
18z%2B14%2B18=%282z%2B1%29%2F6
18z%2B32=%282z%2B1%29%2F6
:
Multiply by 6:
108z + 192 = 2z + 1
:
108z - 2z = 1 - 192
106z = -191
z = -191/106
z = -1.8