Fractions or variables first in solving 1/15k+5 = 1/6k-10

[bikersiggy]

Here is the problem:
1/15k +5 = 1/6k - 10
Do I do the fractions first, then the variables? Do I work on both sides together, or work on each side separate.

1/15k + 1/6k + 5= 1/15k +1/6k - 10
So, do I find the common denominators first?
Any help would be appreciated, I am lost when it comes to finding the missing variable or letter

 

[masters]

Re: Fractions or variables first

Here is the problem:
1/15k +5 = 1/6k - 10
Do I do the fractions first, then the variables? Do I work on both sides together, or work on each side separate.

1/15k + 1/6k + 5= 1/15k +1/6k - 10
So, do I find the common denominators first?
Any help would be appreciated, I am lost when it comes to finding the missing variable or letter

First of all, we need to know if your equation is:

\(\displaystyle \frac{1}{15}k+5=\frac{1}{6}k-10\)

or:

\(\displaystyle \frac{1}{15k}+5=\frac{1}{6k}-10\)

 

[Loren]

Re: Fractions or variables first

1/15k +5 = 1/6k - 10 means \(\displaystyle \frac{1}{15}k + 5 = \frac{1}{6}k - 10\).

I like to eliminate the fractions first by multiplying both sides of the equation (all terms) by the least common denominator, in this case, 30.

If you meant 1/(15k) +5 = 1/(6k) - 10 which is \(\displaystyle \frac{1}{15k} + 5 = \frac{1}{6k} - 10\) the lcd is 30k.

 

[sgtpepper]

Re: Fractions or variables first

I'm assuming you're solving for the variable k. I would first move all the k's to one side and the constants to the other:

(1/15)k + 5 = (1/6)k - 10
(1/15)k + 15 = (1/6)k
15 = (1/6)k - (1/15)k

Now you can pull the k's out:

15 = [(1/6) - (1/15)]*k

Then if you have a calculator:

15 = 0.01*k
15/0.01 = k
1500 = k

Or, if you don't have a calculator:

15 = [(5/30) - (2/30)]*k
15 = [(3/30)]*k
15*(30/3) = k
15*(10) = k
1500 = k


OR...

15 = (1/6)k - (1/15)k

Find a common denominator and subtract the k's:

15 = (5/30)k - (2/30)k
15 = (3/30)k
15 = (1/10)k
15 = k/10
15*10 = k
1500 = k

http://tinyurl.com/6zp8ef

 

[sgtpepper]

Re: Fractions or variables first

I just realized Loren beat me to explaining that, but I'll leave up my post because maybe getting it explained twice makes it clearer to you. I hope I helped!

 

[bikersiggy]

Re: Fractions or variables first

Sgt Pepper,
I am assuming the * mark means multiply. Because you have a minus and a plus sign you had the 5 + 10 to get 15, correct? Sorry, I get confused and why you ad or subtract. Just asking because I am trying to get my basic concepts of doing problems down. I appreciate your help, the letters with numbers are still very challenging for me.

 

[sgtpepper]

Re: Fractions or variables first

You are correct, " * " does indicate multiplication.

Pretend you have:

x + 5 = 3x - 10

the 5 and the 10 are constants and the x's (or k's in your problem's case) are variables. You want to put the constants on one side and the variables on the other. So, let's put the x's on the right side and the constants on the left. To get rid of the x on the left, you have to subtract another x from it to get zero. However, what you do to one side you must do to the other, so:

x - x + 5 = 3x - 10 - x >>>>>>>>>>>>>>>>> [x - x = 0] and [3x - x = 2x]
0 + 5 = 2x - 10

Now move the 10 to the left side - to do that you must add ten to the right side and do the same thing on the left side:

0 + 5 + 10 = 2x - 10 + 10 >>>>>>>>>>>>>>>>>>>>>>>> [0 + 5 + 10 = 15] and [-10 + 10 = 0]
15 = 2x

Then you would finally divide the right side by 2 to get x all by itself - but again, you have to do the same thing to the left side:

15/2 = (2x)/2 >>>>>>>>>>>>>>>>>>>>>> [(2x)/2 = (2/2)*x = (1/1)*x = x]
15/2 = x = 7.5

http://tinyurl.com/5wh95z