Interesting answer given to part of a simultaneous equation

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Probability

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I have equation (2) of a simultaneous equation;

3a = 2b - 1

I am asked to rearrange it and provide two solutions. OK the second one I got; b = 1/2(3a + 1)

But the first I get; a = 2/3(b - 1)

I can't see a problem with that, yet I am told the answer is; 1/3(b - 1)?

How does dividing both sides by 3 = 1/3 instead of 2/3?
 
Probability said:
I have equation (2) of a simultaneous equation;

3a = 2b - 1

I am asked to rearrange it and provide two solutions. OK the second one I got; b = 1/2(3a + 1)

But the first I get; a = 2/3(b - 1) ... that should be a = 1/3 * (2b-1)

I can't see a problem with that, yet I am told the answer is; 1/3(b - 1)?

How does dividing both sides by 3 = 1/3 instead of 2/3?
Click to expand...

If you posted the problem correctly, then both you and your book are incorrect.
 
Probability said:
I have equation (2) of a simultaneous equation;

3a = 2b - 1

I am asked to rearrange it and provide two solutions. OK the second one I got; b = 1/2(3a + 1)

But the first I get; a = 2/3(b - 1)
Click to expand...
NO. The "2" should not be outside the parentheses. Dividing both sides by 3 gives a= (1/3)(2b- 1). If you multiply the 1/3 into the parentheses you get
a= (2/3)b- 1/3.

I can't see a problem with that, yet I am told the answer is; 1/3(b - 1)?
Click to expand...
This is also wrong. If you don't put the 1/3 inside the parentheses, as above, it would be a= (1/3)(2b- 1).

How does dividing both sides by 3 = 1/3 instead of 2/3?
Click to expand...
 
HallsofIvy said:
NO. The "2" should not be outside the parentheses. Dividing both sides by 3 gives a= (1/3)(2b- 1). If you multiply the 1/3 into the parentheses you get
a= (2/3)b- 1/3.


This is also wrong. If you don't put the 1/3 inside the parentheses, as above, it would be a= (1/3)(2b- 1).
Click to expand...

Thanks I was kind of blinding myself with the problem and could not see the wood for the trees.

I did ok on the first part when I said to myself b = 1/2(3a + 1) I put it in brackets not questioning it, then a = 1/3(2b - 1) through me somewhat?

I can see now that it is the same as saying a = 2b - 1 / 3

Thanks guys
 
Probability said:
Thanks I was kind of blinding myself with the problem and could not see the wood for the trees.

I did ok on the first part when I said to myself b = 1/2(3a + 1) I put it in brackets not questioning it, then a = 1/3(2b - 1) through me somewhat?

I can see now that it is the same as saying a = 2b - 1 / 3 .... No it is not ... it is equivalent to

a = (2b-1)/3

Those grouping symbols () are very important.
Thanks guys
Click to expand...
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