How is one supposed to know what order to do things in when solving an algebraic expression?

[ALiteralFlute]

When solving for Y in the expression below, I got the wrong answer by dividing 5 from both sides after the first simplification. I then got the right answer by subtracting 3 from both sides after the first simplification. Although I did the same thing in both attempts, I only got it right in the second attempt. How was I supposed to know that I had to subtract 3 before I could divide 5?

2+(5y+1)=53
5y+3=53
y+3=10.6
y=7.6

2+(5y+1)=53
5y+3=53
5y=50
y=10


(I cannot ask my teacher this question because I do not have a teacher. I never received an education in math. If this question is too simple then what are some resources I can use to understand this instead?)

 

[stapel]

When solving for Y in the expression below, I got the wrong answer by dividing 5 from both sides after the first simplification. I then got the right answer by subtracting 3 from both sides after the first simplification. Although I did the same thing in both attempts, I only got it right in the second attempt. How was I supposed to know that I had to subtract 3 before I could divide 5?

You don't have to. But you do have to do the same thing to both sides -- in their entirety. You can't do the same thing to mere *parts* of the sides.

2+(5y+1)=53
5y+3=53
y+3=10.6

If you are going to divide through by 5, then divide through by 5:

[imath]\qquad 5y + 3 = 53[/imath]

[imath]\qquad \dfrac{5y + 3}{5} = \dfrac{53}{5}[/imath]

[imath]\qquad y + \dfrac{3}{5} = \dfrac{53}{5}[/imath]

[imath]\qquad y = \dfrac{53}{5} - \dfrac{3}{5} = \dfrac{50}{5}[/imath]

 

[topsquark]

When solving for Y in the expression below, I got the wrong answer by dividing 5 from both sides after the first simplification. I then got the right answer by subtracting 3 from both sides after the first simplification. Although I did the same thing in both attempts, I only got it right in the second attempt. How was I supposed to know that I had to subtract 3 before I could divide 5?

2+(5y+1)=53
5y+3=53
y+3=10.6
y=7.6

2+(5y+1)=53
5y+3=53
5y=50
y=10


(I cannot ask my teacher this question because I do not have a teacher. I never received an education in math. If this question is too simple then what are some resources I can use to understand this instead?)

You can pretty much come up with whatever method you like, so long as its Mathematically viable. But there's a reason you are given courses: someone(s) else has sat down and come up with algorithms to help you. These are what you learn in your classes.

For now, just try to learn the methods. As you progress and learn more, you will see that you can vary them a bit to suit your specific problem.

So if you are solving a linear equation, the routine is to get simplify each side, then get the variable you are solving for on one side of the equation, then manipulate it so that you can get that variable alone. (Actually, that pretty much calls it for most problems.)

But as time goes on you find you can vary your approach. One I saw yesterday (on SyberMath)
[imath](x+1)^4 = x^4[/imath]
Method 1:
[imath]x^4 + 4 x^3 + 6 x^2 + 4x + 1 = x^4[/imath]

[imath]4 x^3 + 6 x^2 + 4x + 1 = 0[/imath]

Now solve the cubic.

Method 2: Divide both sides by [imath]x^4[/imath]:
[imath]\dfrac{(x+1)^4}{x^4} = \left ( \dfrac{x+1}{x} \right )^4 = 1[/imath]

Now take the 4th root of both sides, and solve for x.

The first method is "standard" but the second one is easier, but specific to the this problem.

-Dan

 

[Steven G]

When solving for Y in the expression below, I got the wrong answer by dividing 5 from both sides after the first simplification. I then got the right answer by subtracting 3 from both sides after the first simplification. Although I did the same thing in both attempts, I only got it right in the second attempt. How was I supposed to know that I had to subtract 3 before I could divide 5?

2+(5y+1)=53
5y+3=53
y+3=10.6

No, you did not divide both sides 5. Yes, you divided the right hand side by 5. However, you only divided part of the left side by 5!

Consider this: 4+8 =12 is an obviously true statement.
Now I divide by 4 and get 1+8 = 3 (note that I divided 4 by 4 and 12 by 4). Well 1+8 does not equal 3!

You need to divide the whole left hand side by 4. Now 4+8 divided by 4 is 1+2=3 which is 12/4.

 

[jonah2.0]

Beer induced reaction follows.

... I never received an education in math. ...

I guess that's possible but I can't help but wonder as to what were the conditions that made such a circumstance possible. Perhaps that statement is an exaggeration as you are able to to do basic math stuff of subtraction and division.