Fractions and algebra multilplying... PLEASE HELP EXAM IN FEW HOURS~!?

Question

2/3 ( 5y -1 ) = 1/2 ( 7y + 2 ) - 5
I have no clue what to do... i get to a certain point which i think may be wrong O_o''

Answer 1

Look at the fractions. Common denominator is 6. So multiply all terms by 6. Get:

6 • 2/3 (5y-1) = 6 • 1/2 (7y+2) - 6 • 5
4 (5y-1) = 3 (7y+2) - 30
20y - 4 = 21y + 6 - 30
20y - 4 = 21y - 24
-4 = y - 24
20 = y

Answer 2

The main goal of this problem is to solve for your variable, in this case that variable is y. To do this you want to get all terms with y on one side of the equation, and all terms without y on the other side. So the first step for this equation would be to distribute your fractions outside of the parenthesis. When you do this to both sides you should have something that looks like this.
(10/3)y - 2/3 = (7/2)y + 1 - 5
Now you can get all of ther terms with y on one side. Subtract the term (7/2)y from both sides of your equation. You will be left with this.
(10/3)y - (7/2)y - 2/3 = 1 - 5
Now add 2/3 to both sides of the equation so that you can have all of the y terms on one side and the other terms on the other side.
(10/3)y - (7/2)y = 1 - 5 +2/3
Now to keep things less confusing, we will simplify both sides. In other words make it so both sides have the same common denominator. On the left side change 10/3 to 20/6, and change 7/2 to 21/6. DO NOT FORGET THE NEGATIVES! On the right side we will change 1 to 6/6, 5 to 30/6, and 2/3 to 4/6. Now that all terms on both sides have the same denominator, we add and subtract the numerator to simplify the equation. (numerator is the top part of a fraction, denominator is the bottom part of a fraction). Once you have done this, you should be left with this.
-(1/6)y = -20/6
Approaching the final steps to solve this equation, multiply both sides by negative one (-1) so that it is easier to look at.
(1/6)y = 20/6
Lastly multiply each side by 6 and you will have your answer. You multiply by 6 because you ultimately want to get y on one side alone with no other terms and no coeffecients. This gives you your answer.
y = 20
Incase you are unsure at all, or even if you are not, it is always a good habit to plug your answers back into your equation to make sure that you are correct.
2/3 (5(20) - 1) = 1/2 (7 (20) + 2) - 5
2/3 (100 - 1 ) = 1/2 ( 140 + 2) -5
2/3 (99) = 1/2 (142) -5
66 = 71 - 5
66 = 66 Correct!
Congradulations, I hope that this has been helpful for you and good luck on your exam.

Answer 3

2/3(5y) - 2/3 = 1/2(7y) + 1 - 5
+ 4 both sides
2/3(5y) + 3 1/3 = 1/2(7y)
multiply out
10/3y + 10/3 = 7/2y
common denominator is six, so
20/6y + 20/6 = 21/6y
subtract 20/6 from both sides
20/6 = 1/6y
Multiply both sides by six
20 = y

Answer 4

I'm working this out one babystep at a time, 'cause I can barely remember how to do this.

Please confirm this answer with other answers before you trust it!!

I hope this gives you enough details so you can go back and see exactly how I solved it, if my answer turns out to be correct:

2/3 ( 5y -1 ) = 1/2 ( 7y + 2 ) - 5

first get rid of those parentheses if you can:
10/3y - 2/3 = 7/2y + 2/2 - 5

simplify the 2/2 by making it a 1:
10/3y - 2/3 = 7/2y + 1 - 5

add the +1 and the -5:
10/3y - 2/3 = 7/2y - 4

get rid of the -2/3 on the left side by adding 2/3 to both sides:
10/3y - 2/3 + 2/3 = 7/2y - 4 + 2/3

10/3y = 7/2y - 3 1/3

get rid of the 7/2y on the right side by subtracting 7/2y from both sides:
10/3y - 7/2y = 7/2y - 3 1/3 - 7/2y

10/3y - 7/2y = - 3 1/3

next, figure out how to get a common denominator for those two numbers on the left... i used 6 for my common denominator:
20/6y - 21/6y = - 3 1/3

- 1/6y = - 3 1/3

now you want to isolate y, so get rid of the -1/6y by dividing both sides of the equation by -1/6:
(-1/6y) divided by (-1/6) = (- 3 1/3) divided by (-1/6)

y = (- 3 1/3) divided by (-1/6)

i wanted to get both numbers to be simple fractions:
y = (-10/3) divided by (-1/6)

to divide two simple fractions, you flip the second fraction and multiply (if i remember correctly):
y = (-10/3) multiplied by (-6/1)

then you get:
y = 60/3

simplify that fraction:
y = 20

Good luck and God bless you! :)

Answer 5

Expand both sides of the equations.
10/3 y - 2/3 = 7/2 y + 1 - 5
10/3 y - 2/3 = 7/2 y - 4

then bring all the numbers with the algebra y to the left hand side.
10/3 y - 7/2 y = -4 + 2/3
20/6y - 21/6y = -10/3
-1/6y = -10/3

If you can use a calculator, then use it. If not,
multiply both side of the eqaution by 6 to remove the denominator like this:

-y = -20

Then, multiply both sides with (-):
y = 20

Tadah!

Answer 6

I believe you are trying to figure out the value of y:

Step 1:
Mulitply both sides of the equation by 6 to get whole numbers and make the equation simplier.

So after multiplying both sides of the eqn by 6:

4(5y-1) = 3(7y+2) - 30

Step 2: Expand

20y - 4 = 21y + 6 - 30

Step 3: Bring the unknown to one side of the eqn, so I bring 20y to my right and all the figures to my left

21y-20y = 30 - 6 - 4

Thus, y = 20! ;-) Hope it helps. Good luck for your exams!

Answer 7

multiply the 2/3 and 1/2 by everything inside the parenthesis. You should get (10/3)y - 2/3 = (7/2)y +1 - 5. Combine the terms with y on one side and everything else on the other, then divide by any constant in front of y to get y alone. I came up with y= 20. Isn't math fun? hehehe

Answer 8

(2/3)( 5y -1 ) = (1/2)( 7y + 2 ) - 5

First clear the denominators

2*2(5y - 1) = 3*(7y + 2) - 5*3*2
20y - 4 = 21y + 6 - 30 = 21y - 24
20 = y

Answer 9

it's best to get rid of the fractions. that's what i always did. so multiple both sides by a least common multiple. so... multiple each by 6. then you get...

4(5y-1)=3(7y+2)-30

work from there to solve for y.

20y-4=21y+6-30
-4=y-24
y=20

Answer 10

10/3y-2/3=7/2y+1-5 -->
(7/2-10/3)y=4-2/3 -->
(1/6)y=10/3 -->
y=6*10/3=20