I need help figuring out an algebraic equation?

Question

5(2y-1)=3(y-4)
If you can solve this and explain to me how you got the answer or show you work that would be awsome im really having a hard time catching on to this kind of math

Answer 1

You want to get y all by itself on either the left or right side of the equals sign (since the right will be the exact same thing as the left -- that is what "equals" means -- it doesn't matter which side you pick).

I have 5 times (2y - 1) so you can "distribute" the five which means I multiply the 5 to each term inside the parentheses.
5*2y = 10y and 5*(-1) = -5 so on the left side of the equation you now have 10y - 5.

Repeat for the right side. 3 times (y - 4) is 3*y and 3(-4) is 3y - 12.

Now we have
10y - 5 = 3y - 12

Think of it now like those old-fashioned scales (see http://www.abestscale.com/image/534730.jpeg for a picture).

To maintain both sides being equal, I have to do the same thing to both sides. On the left side of the scales, I have ten "y"s and a negative five. On the right side of the scale, I have three "y"s and a negative twelve. If I take away three "y"s from both sides of the scale, it will still be balanced, but I will only have "y"s on one side.

(10y - 3y) - 5 = (3y - 3y) - 12
7y - 5 = -12

Y is almost by himself!!!! I just need to get rid of the -5 and the 7. The left side reads, "Seven ys minus 5" but I only want to know what one y is. Add five to both sides (do the opposite of what is happening to get rid of something -- since five is being subtracted, we add it to boths sides).

7y - 5 = -12
7y (-5 + 5) = (-12 + 5)
7y = -7

If I divide both sides by 7 (since that is the opposite of multiplying by 7), I will know what a single y is!!

(7y)/7 = -7/7
y = -1

Finally, CHECK YOU ANSWER!!!!! As you get further along in math, sometimes you will have done everything right but find out by checking that the answer will make your equation blow up (not a pretty sight -- we call that an "extraneous solution").

Whereever there is a "y" in the original equation, you are going to put in -1, then follow order of operations.

5(2(-1) - 1) = 3(-1 - 4)
5(-2 - 1) = 3(-5)
5(-3) = -15
-15 = -15

So y really does equal -1!!!!!

Hope that helps!

Answer 2

10y-5 = 3y-12 First you need to do a multiplication,
12-5= 3y-10y After you need to put in one side all numbers
-7y = 7 with variables and make an algebraic sum
y = -7/7 Now you need to separate the variable, if you
y = -1 see -7 is multiplying variable "y" then go to the other side dividing. Now you see that the value of "y" is -1, if you substitute that value in the original equation you can see that both side of the equation are the same. That is the prove that the value of "y" is correct.

5(2(-1) - 1) = 3((-1) -4)
5(-2 -1) = (-3 - 12)
-10 - 5 = -15
-15 = -15

Answer 3

The idea is to solve for the variable (y). To do that you have to "isolate" it on one side of the equals sign.

1. Do all the multiplication first:

(5*2y) - (5*1) = (3*y)-(3*4)
10y - 5 = 3y -12

2. Move the y values to one side and all the constants to the other side of the equals.

10y -3y = -12 + 5
7y=-7

3. Solve for y
7y *1/7 = -7 * 1/7
y = -1

4. Check your answer by plugging the value into the original equation.

5[(2*-1) -1] = [3(-1-4)]
5(-2-1) = 3(-5)
-15 = -15

Answer 4

When solving this type of problem, you want to first multiply both sides. The problem: 5(2y-1) = 3(y-4). Now, multiply everything out like this, 10y-5 = 3y-12. Now you want to get the "y" terms on one side and set them equal to the numeric terms, like this 10y-3y = -12+5 (remember that when you bring terms to the left/right side of the = sign their signs change). Now continuing with the problem: 10y-3y = -12+5 we get 7y = -7. Now we have to set everything equal to y, and we do this by dividing both sides by 7. Like this, 7y/7 = -7/7 which gives us this y = -1 so y is equal to -1. So if you put -1 back into the original equation you will get -15 is equal to -15. So the answer is {y = -1}

Answer 5

The first thing that you want to do is distribute. All that means, is multiply what's outside of the parentheses, by what's inside. It's easier just to show you.

5(2y-1)=3(y-4) Multiply 5 by 2y and then multiply 5 by 1. Remember to keep the - sign in there though! Do the same for 3(y-4).
10y-5=3y-12

Then you what to get y=? So you need to either add 5 to both sides, or 12 to both sides, because the opposite of -5 and -12 is +5 and +12. Let's add 5, I like 5.

10y-5+5=3y-12+5
10y=3y-7

Now you want to get rid of the 3y on the right side. So you need to subtract 3y from both sides.

10y-3y=3y-7-3y
7y=-7

Now to turn 7y into 1y, you want to divide both sides by 7. You can't subtract 6y from both sides because then you end up with -6y on the right side of the equation.

7y/7=-7/7
y=-1

There you go! Message me if you have any questions!

Answer 6

this problem requires using the distributive property. you have to 'distribute' the quantity outside the parentheses over each term inside the parentheses -- that means you multiply each term inside by whatever is outside.

5(2y - 1) = 3(y - 4)

10y - 5 = 3y - 12 apply distributive property

10y - 5 + 5 = 3y - 12 + 5 subtract 5 from both sides

10y = 3y - 7 simplify by adding constants

10y - 3y = 3y - 3y - 7 subtract 3y from both sides

7y = -7 simplify

y = -1 divide both sides by 7

to successfully do this type of problem, write out each step so you can clearly see what you are doing. Don't skip steps until you get to be very good at these problems!

Answer 7

5(2y-1) = 3(y-4)

multiply the 5 into its paratheses and the 3 into its paranthese
5(2y)-5(1) = 3(y)-3(4)
10y-5 = 3y-12

add 5 to both sides

10y-5+5 = 3y-12+5
10y = 3y-7

subtract 3y from both sides

10y - 3y = 3y-7-3y
7y = -7

divided both sides by 7

7y/7 = -7/7
y = -1

Answer 8

5(2y-1)=3(y-4)
multiply 5 in parenthesis and other side 3 in parenthesis

10y-5 = 3y-12
do 10y-3y and other side do -12+5

7y = -7
divide both sides by 7

y = -1



5(2y-1)=3(y-4)
10y-5=3y-12
7y=(-7)
y=(-1)

Answer 9

First step is to distribute both sides of the equation. (5)(2y) and (5)(-1)= 10y-5
then (3)(y) and (3)(-4)= 3y-12
Your equation becomes 10y-5=3y-12
Next get the variable to one side by subtracting 3y from both sides. Now you have 10y-3y-5=3y-3y-12, which is 7y-5=-12
then you would add 5 to both sides, ie 7y-5+5=-12+5, which is 7y=-7
Last step is to divide both sides by 7 to isolate the y.
Your answer is thus y=-1

Answer 10

y=-1