i have doubt about math rule

Question

for example

(120x+22)/3=(300x+25)/6

(120x+22)/3*6/(300x+25)

(120x+22)*2/(300x+25)
(240x+44)/(300x+25)

now (300x+25)this term goes other side

(240x+44)=(300x+25)           

44-25=300x-240x

     19 =x

my doubt is when we sent any number or variable it change its sign. So why we didt change (300x+25) this term sign

please my concept about this

Answer 1

Yes, Amey, don't get mixed up between addind and subtracting vs. dividing and multiplying. In your very first step, you didn't change the 6 to -6. Why? Because you multiplied!

 

Let's look at some simpler examples.

 

2x + 5 = 21

 

I need to first move the 5 to the other side. How do I do that? It's added, so I subtract it from both sides. Now I have

 

2x + 5 - 5 = 21 - 5

 

Since 5 - 5 = 0 on the left, we efficient math people don't write in 0. Instead we are left with 2x = 16.

 

What's the next step? We need to get rid of the 2. 2x means 2 times x, so we divide both sides by 2.

 

2x/2 = 16/2

 

2/2 = 1, buuuuuut, we again don't write 1x, we just write x, so we are left with x = 8.

 

To summarize, adding or subtracting is going to change the sign on the other side, because we are doing the opposite operation. Multiplying and dividing, while also the opposite operation, does not change the sign.

 

Hope this makes sense!

 

 

Answer 2

Look, everyone, it's very simple.  You must know the definition of term.

 

Then you can understand the rule that "when a term is taken to the opposite side of an equation, its sign changes to the opposite."

 

Example 2x + 4 = 0

     then  2x       = -4

 

The proof of this rule is to add the opposite of any term to both sides of an equation.

 

I hope that this is clear.

Answer 3

What you say by "when we sent any number or variable it change its sign" has no meaning in mathematics.

 

Here you are discussing an equation. Every eaquation is maintained by Left Hand Side (L.H.S)= Right hand Side (R.H.S)

In your probelm you missed all EQUAL signs from line 2 to where you have written "now (300x+25)this term goes other side" I am applying the EQUAL sign in each line that will explain what you are missing.

(120x+22)/3=(300x+25)/6
(120x+22)/3*6/(300x+25)=1 [ here we have divided both sides by (300x+25)/6, R.H.S. =1]

(120x+22)*2/(300x+25) =1  [here all the operations has been done on L.H.S hence R.H.S remains same as previous line]     
(240x+44)/(300x+25) =1[here all the operations by adjusting coefficients and constrants has been done on L.H.S hence R.H.S remains same as previous line]  
now (300x+25)this term goes other side
(240x+44)=(300x+25) [ here we multiply each side by the denominator of L.H.S, change of sign means addition and subtraction, therefore while we are multiplying we just check the sign of constants and coefficients in operation. In the present line the constant at R.H.S is positive.  Thus the multiplication did not change the sign of denominator of the L.H.S]
44-25=300x-240x [ here 240x has been subtracted from both the sides. At LH.S it has been cancelled, you could have added that step. That would have kept your concepts clear. We do not change signs if we change side. We change side to reach a solution for x either by adding terms, subtracting terms, and also multiplying by and dividing by terms. The sign of the resultant term changes depending on the operation( adding, subtracting, multiplying, dividing) and the signs of the term (positive or negative) involved in the operation. Thus 25, too has been subtracted from both sides.]
19 =x

 

You can go through answers I have given in this forum. Whenever I solve an equation I ecplain all the operations. it will clear your conception about why sign changes onn changing sides and why they do not change.