manipulation of in math on equations!

R

Ryan$

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Hi guys! sorry for that but I really find it hard and struggle it everyday!! every moment!
if I have an equation like X=Y+5
and I know that we can multiply this equation by anything I want, but it didn't ring in my head while solving .. what do I do to get the idea of?

what's confusing me ...when I can multiply an equation on its two sides? maybe if I know when I can multiply and when not ..then I can manage and handle it while solving ..

exactly I'm asking it's allowed to multiply the equation?!
 
Hi guys! sorry for that but I really find it hard and struggle it everyday!! every moment!
if I have an equation like X=Y+5
Click to expand...
Okay, you have that equation. What do you want to do with it?

and I know that we can multiply this equation by anything I want, but it didn't ring in my head while solving .. what do I do to get the idea of?
Click to expand...
Yes, you can multiply (both sides of) an equation by any thing you want and it will remain a true equation. But why would you want to?

what's confusing me ...when I can multiply an equation on its two sides? maybe if I know when I can multiply and when not ..then I can manage and handle it while solving ..
Click to expand...
Always! You always can multiply both sides of an equation by the same thing. The question you should be asking is whether or not you want to! And that depends on what you want to do! Solve an equation? What equation? You referred to "X= Y+ 5" above. Do you want to solve for Y? Then, while I COULD "multiply both sides by the same thing" there is no reason I would WANT to! To "solve for Y" means to get an equation like "Y= something" where Y is alone on one side of the equation. I the equation, X= Y+ 5, Y is not alone because 5 is added to it. The opposite of "adding" is "subtracting". To solve for Y I would not "multiply" by anything- I would subtract 5 from both sides to get X- 5= Y.

exactly I'm asking it's allowed to multiply the equation?!
Click to expand...
Again, it is not a matter of being "allowed". You are always allowed to do anything you like*, as long as you do it to both sides of the equation. It's a question of whether or not you should do it- whether it would help solve the problem.

(* Well, you are not allowed to "divide by 0" but. other than that, feel free!)
 
[MATH]x = y + 5[/MATH] means that the number named temporarily as x has the same numeric value as the number temporarily named y plus 5.

So when I multiply both sides of the equation by, for example, 7. I am multiplying 7 by the same number on each side so I get the same numeric value on both sides. And this is true of any number. It really is that simple. As Halls says, you can do it whenever you want. Whether it is useful to do depends on where you want to go.

What you can do and what you need to do are two different things.

Some of the basic things that you always can do in algebra are:

[MATH]a = b \iff a + c = b + c.[/MATH]
[MATH]a = b \iff a - c = b - c.[/MATH]
[MATH]a = b \iff a * c = b * c.[/MATH]
[MATH]\text {Provided } c \ne 0,\ a = b \iff \dfrac{a}{c} = \dfrac{b}{c}.[/MATH]
The things you are allowed to do in algebra make sense because they are just generalizations of what always works with any numbers. The question is not whether you can do one of these universally valid actions, but whether it helps you find the desired answer to do it.

Do you seriously doubt

[MATH]9 = 4 + 5 \implies 63 = 28 + 35 \implies 7 * 9 = 7 * 4 + 7 * 5 = 7 * (4 + 5).[/MATH]
 
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