You can
put this solution on YOUR website!It's a little riddle, that's all. y is a symbol for a number. It's just a number. Now the equation (two things equal) says
3y + 4 is equal to 5y +6.
That means: there is a number y that fits the following description:
If you multiply y by 3 and add 4 you get a resulting number.
If you multiply y by 5 and add 6 you get a resulting number.
What does y have to be so that those two resulting numbers are equal?
Algebra is the study of such questions, and has developed some "rules" that allow you to find the answer by manipulating the algebraic expressions. (An algebraic express is an arithmetic experssion like 2 + 3 times 4, but with one or more of the numbers replaced by a name. Usually in simple cases the name is a single letter, like "y.")
For example: a basic rule is that if two numbers are equal (6=6) and you add a number to one of them, you only keep them equal if you add the same number to the other one. This is usually stated as "Equals added to equals are equal." (Namely, 6=6 added to 3=3 gives 9=9.) Cute, no? So if you add 3 to one of the 6's, you have to add 3 to the other one, giving 9=9.
Now we don't have 6=6; we have 3y+4 = 5y+6. But each side is just a number!
Let's say we add something to the left expression (3y+4). But what? Well, how about adding
to it?
. But 4 no longer equals 5y+6. We have to add -3y to the other expression, too. -3y+5y+6 = 2y+6. (If you don't believe this, just remember what 5y means: y+y+y+y+y. And -3y means -y-y-y. So you end up with 2y.
Now we still have an equation, namely, 4 = 2y+6.
At this point we can add -6 to both sides! This gives -2 = 2y.
What is true about adding the same number to both sides is also true if we multiply both sides by the same number (since multiplying is just adding over and over). So let's multiply both sides by 1/2.
We get -1 = y. Egad, the "answer."
Naturally, the numbers you pick to add to both sides, or multiply by both sides, are selected with skill, intelligence, and guesswork so as to get the "answer." But practice will show you how to pick good numbers to work with.
Anyway, I hope this helps.
You can
put this solution on YOUR website!3y+4=5y+6
Let's see what we can do to help you play ball.
First thing to remember; the word "algebra" is nothing but a scary word. Do not let it scare you, so many kids think just like you. But it is not hard to get.
OK, let's get back to the problem:
The final outcome is to find what y=,
So we want to get the y's on one side and the numbers on the other.
To do this, first you will subtract the 4 from the left side; and one of the MOST IMPORTANT THINGS TO REMEMBER; WHAT YOU DO TO ONE SIDE YOU DO THE EXACT OPERATION TO THE OTHER.
So with that in mind if we subtract the 4 from the left side we have to subtract 4 from the right.
3y+4-4=5y+6-4
We get:
3y=5y+2
Now lets get the 5y on the other side, to do this you need to subtract the 5y from the right side, and remember WHAT YOU DO TO ONE SIDE YOU DO TO THE OTHER, so we will subtract 5y from the left side also,
3y-5y=5y+2-5y
We now have: -2y=2
We still do not know what the y =, so we are not done.
Now we need to get that y by itself. So we need to get rid of the -2. To do that we do the opposite operation, which is divide. Because y is being multiplied by -2, so we need to divide by -2 so we can have y alone. And remember WHAT YOU DO TO ONE SIDE YOU HAVE TO DO TO THE OTHER. So we will divide the right side by -2 also.
Now you cancel out the -2 n the left:
y=-1
I really hope this helps you so you can play ball! Let us know if you need more help.
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