Grr...Algebra

[TyraBanksIsFierce]

I have a test for all this stuff on tuesday, ive got most of it down except theres a few things i cant work out, like this problem:



This ones a linear equation,

you have to find out what X is

i always end up with 1.25 but the answer is 6.25..

I did a similar question and got it right, except it was more straightforward with no brackets and addition instead of subratction

Can you help
Thankss

Discuss
-Algebra
-Exams
This Problem

Ok, so first you want to get a common denominator to subtract fractions. so multiply the top and bottom of the first fraction by 3/3 and the top and bottom of the second fraction by 2/2. So you get (6x-9/6)-(10x-10/6)=-4. Subtract the numerators to get -4x+1/6=-4. Multiply both sides by 6 to clear the fraction. So now you have -4x+1=-24. Subtract 1 from both sides and you get -4x=-25. Divide by 4 to get x=-25/-4. The negatives cancel and you get 25/4 which is 6.25.

[ArcusPuer]

i dont see how it is 6.25
i got 1.25 as well.
perhaps the answer is wrong........?

[ArcusPuer]

Originally Posted by Midnight Angel

Ok, so first you want to get a common denominator to subtract fractions. so multiply the first fraction by 3 and the second fraction by 2. So you get 6x-9/6 - 10x-10/6=-4. Subtract the numerators to get -4x+1/6=-4. Multiply both sides by 6 to clear the fraction. So now you have -4x+1=-24. Subtract 1 from both sides and you get -4x=-25. Divide by 4 to get x=-25/-4. The negatives cancel and you get 25/4 which is 6.25.

wait how did u get the +1?
isn't it -9-10.... which is -19....

[Owen]

It comes down to simplification. I'd start by multiplying that five on the top of the second fraction through what's in the parenthases.

(2x-3)/2 - (5x-5)/3 = -4

I'd then turn the whole left side of the equation into one fraction by multiplying the first fraction by 3/3 and the second fraction by 2/2. That way, you are effectively multiplying each fraction by one, which does not change the equation at all.

(3/3)•(2x-3)/2 - (2/2)•(5x-5)/3 =-4
(6x-9)/6 - (10x-10)/6 = -4

We can now combine those two fractions into one fraction.

((6x-9) - (10x-10))/6 = -4
(6x-9-10x+10)/6 = -4
(-4x+1)/6 = -4

We now multiply both sides by six to get rid of the fraction

-4x+1 = -24

We no subtract one from both sides...

-4x = -25

And divide both sides by -4.

x = -25/-4 = 6.25

Here's the math all together so it looks like work you would do on a homework assignment.

(2x-3)/2 - 5(x-1)/3 = -4
(2x-3)/2 - (5x-5)/3 = -4
(3/3)•(2x-3)/2 - (2/2)•(5x-5)/3 =-4
(6x-9)/6 - (10x-10)/6 = -4
((6x-9) - (10x-10))/6 = -4
(6x-9-10x+10)/6 = -4
(-4x+1)/6 = -4
-4x+1 = -24
-4x = -25
x = -25/-4 = 6.25

Edit: Damn! Beaten to it.

Originally Posted by ArcusPuer

wait how did u get the +1?
isn't it -9-10.... which is -19....

Distribute the negative sign. It's -9--10. Two negatives make a positive.

[TyraBanksIsFierce]

Originally Posted by Midnight Angel

Ok, so first you want to get a common denominator to subtract fractions. so multiply the top and bottom of the first fraction by 3/3 and the top and bottom of the second fraction by 2/2. So you get 6x-9/6 - 10x-10/6=-4. Subtract the numerators to get -4x+1/6=-4. Multiply both sides by 6 to clear the fraction. So now you have -4x+1=-24. Subtract 1 from both sides and you get -4x=-25. Divide by 4 to get x=-25/-4. The negatives cancel and you get 25/4 which is 6.25.

wow, i know what I did wrong now, I got -19 out of the -9 minus the -10

forgot that negative a negative means is adding.

Thank You!!

[TyraBanksIsFierce]

Oh and thanks to anyone else who tried!

[Owen]

Originally Posted by ArcusPuer

wait how did u get the +1?
isn't it -9-10.... which is -19....

When you subtract a negative number, you add it's possitive version, so if you subtract -10, you are adding 10.

[Owen]

Originally Posted by TyraBanksIsFierce

wow, i know what I did wrong now, I got -19 out of the -9 minus the -10

forgot that negative a negative means is adding.

Thank You!!

Argh! Beaten again.

[ArcusPuer]

ok i get it know, i forgot that u had to multiply the second fraction by the negative.

[starfish]

Can you show us your solution so we can see where you went wrong.

I worked it out and got x = 6.25


Here is my solution.

[sdc91]

The first step you should do is multiply everything by 6 to get rid of the fractions... starfish's solution works, but it makes it waaaaaaaaay easier to make mistakes.

[Amy]

Algebra is evil.

[Apocalypte]

If any of you want a fright, my thesis for my CS degree will be based around a computational problem in algebra.
Oddly enough, I'm probably a better mathematician than programmer...