Thread: I'm unsure of some problems

1. I'm unsure of some problems

these are problems that can either be answered with a decimal or fraction, but the book only provides the fraction answer and i do decimal methods, so im worried i may have done something wrong...
numbers written like this: 1/2, 4/5
15. -2/3(6 - 2a)=6
multiply by -3/2
6-2a=-9
-6 from each side
-2a=-15
divide each side by -2
a=7.5
the book says the answer is 15/2
18.16=5(1-x)
distribute 5...
16=5-5x
-5 from each side..
11=-5x
divide each side by -5
-2.2=x
the book doesnt give an answer, so i'm even more worried about its correctness, lol.
20.n-4(1+5n)=-2
distribute -4...
n-4-20n=-2
n-20n=2
1n-20n=-19n
-19n=2
divide each side by -19
n=-0.105263158
book doesnt provide an answer, and the sheer length of the decimal has me worried, lol
and finally,
22.6m-3=10-6(2-m)
10-6=4
distribute 4
6m-3=8-4m
10m-3=8
10m=11
divide each side by 10...
m=1.1
the main thing im worried about here is that the teacher said between problem 17 and 22 there was 1 problem with 'all numbers' as an answer and 1 problem with 'no solutions' as an answer. i got the all numbers one, but the answers to all the others, unless i did something wrong, are
17. -2=z
18. 2=h
19. all numbers
20. r=-5
21. x=-15
22. m=1.1
so, 22 seems the most likely to have been the one i made a mistake in, due to the fact all the others have solid non-decimal answers.

2. these are problems that can either be answered with a decimal or fraction, but the book only provides the fraction answer and i do decimal methods, so im worried i may have done something wrong...
numbers written like this: 1/2, 4/5
15. -2/3(6 - 2a)=6
multiply by -3/2
6-2a=-9
-6 from each side
-2a=-15
divide each side by -2
a=7.5
the book says the answer is 15/2 -----Okay. But what is 15/2? Is it 7.5?

---------------------------------
18.16=5(1-x)
distribute 5...
16=5-5x
-5 from each side..
11=-5x
divide each side by -5
-2.2=x
the book doesnt give an answer, so i'm even more worried about its correctness, lol.

16 = 5(1-x),
16 =? 5(1 -(-2.2))
16 =? 5(1 +2.2)
16 = 5(3.2)
16 =? 16
Yes, so, OK, your x = -2.2 is correct.

---------------------------
20.n-4(1+5n)=-2
distribute -4...
n-4-20n=-2
n-20n=2
1n-20n=-19n
-19n=2
divide each side by -19
n=-0.105263158
book doesnt provide an answer, and the sheer length of the decimal has me worried, lol

Why not just n = -2/19 then?
After -19n = 2,
n = 2/(-19)
n = -2/19.

Check that by substituting it into the original equation. (It is correct, I checked.)

-----------------------------
and finally,
22.6m-3=10-6(2-m)
10-6=4 ----------------------this not correct. The -6 is connected to the (2-m). You cannot treat the -6 as separate.
Here is the continuation,
distribute -6,
6m -3 = 10 -12 +6m
subtract 6m from each side,
-3 = -2
Whoa, no more unknown?
Besides, -3 is not equal to -2 either.
So, the given equation has no solution.

6m-3=8-4m
10m-3=8
10m=11
divide each side by 10...
m=1.1
the main thing im worried about here is that the teacher said between problem 17 and 22 there was 1 problem with 'all numbers' as an answer and 1 problem with 'no solutions' as an answer. i got the all numbers one, but the answers to all the others, unless i did something wrong, are
17. -2=z
18. 2=h
19. all numbers
20. r=-5
21. x=-15
22. m=1.1
so, 22 seems the most likely to have been the one i made a mistake in, due to the fact all the others have solid non-decimal answers.