when you subtract a variable from a whole number and a variable:example x+23=2x+45 why does the 2x become 0?

Question

I need to understand the rules of basic algebra. I understand the answer, I need to understand why it is the answer. x+23=2x+45

      x-x+23=2x-x+45

        23=x+45. why does the 2x become just x ? why is the answer not just 2?

Answer 1

This is easier to understand if you write it as x+23=x+x+45. Your description seems to imply that 2x minus x should be 2. 2x is (x+x).  If you subtract x from (x+x) you get x. if you subtract x from (2+x) you get 2.

Answer 2

Hi Kelvin,

To answer your question, I'd like to start with a simpler example:

First of all, make sure that when you're solving an equation that you always do the exact same thing to both sides of the equal sign. No matter how much you add, subtract, multiply, or divide, if you do the exact same thing to both sides of the equal sign, then both sides will still be equal to each other.

Start with  x = 4, and try adding 2 to both sides of the equal sign

x + 2 = 4 + 2

so x + 2 = 6

Let's solve for x to make sure that x=4 is still true.

If you subtract 2 from both sides of the equal sign, then you get x = 4 again

x + 2 = 6

   -2     -2

x  (+ 0) = 4

x = 4

-----------------------------

Now let's look at your problem:
x+23=2x+45

First we want to get all of the x's alone on one side of the equal sign, so we can find out the value of x.

On the left we have 1 x, and on the right side of the equal sign we have 2 x's.

If we subtract 1 x from each side, how many x's will be left on each side?

  1x + 23 = 2x + 45

-1x           -1x       

0x + 23  = 1x + 45

Now we have no x's left on the left side of the equal sign because if we have an x and then subtract an x, we'll have 0 x's left. 

On the right side of the equal sign, we had 2 x's and subtracted 1 x, so we have 1 x left.

 

Now we can finish solving the equation to find out the value of x, by subtracting 45 from each side (to get the x alone).

 23 = x + 45

-45        -45

-22 = x + 0

x = -22

 

I am a tutor near you, so please don't hesitate to contact me you have any other questions! :-)

-Jamie

 

 

 

Answer 3

Another way to think abou this is to write the "x" terms in one color and the non-x terms in another. You are combining like terms...in other words only adding and subtracting the like colors.

Answer 4

To answer that question " 2x does not become 0 " The idea is to get x by it self. You are solving for X

Answer 5

One of the basic rules for algebra is subracting like terms. 2x and x are like terms believe it or not. Another basic algebraic rule is: there is ALWAYS an implied or imaginary 1 attached to a variable when there is not a number already attached to it (like the 2x). Thus: 2x-1x = x (just plain x). Remember, we are trying to figure out the numerical value for x. So do not forget to subtract from both sides of the equation (which you said you already understand).

x + 23 = 2x + 45

-x + 23 = -x + 45

- 45 = x - 45

-22 = x