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why do you have to subtract on both sides of the equation when solving a algebra problem

for example x + 23 = 45

Subtract 23 from each side x + 23 - 23 = 45 - 23
 im not sure how to do this at all and x=22

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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 Just like you did:
 
 
   X+ 23 = 45
 
   X+ 23- 23 = 45 -23
 
    X = 22.
 
   One quicker way is use move over:
 
     X + 23 = 45       / You are going to solve for X , you have to keep all X's in one side.
 
     So now, you say Move 23 to the other side and change the sign.
 
      X = 45 -23 = 22.
 
      This is equivalent of adding or subtracting same quantity from both sides, and from the fact that subtraction and addition are opposite of each other.
 
     Sometimes you need to solve a variable in terms of the rests.
 
      P = 2L +2w ,  solve L:
 
      P - 2w = 2L         / Keep L in one side, and move rest to the other side, change the sign when moving . 
                               / one quantity to the other side.
       L = P- 2W
                2
 
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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Dear Charlotte,
 
Usually, solving an equation means solving it for an unknown.
 
In this example
 
x + 23 = 45
 
the unknown is x.  Now, you have to ask yourself:  "What do I have to do in order to isolate x on the left-hand side of the equation?"
 
The answer is "subtract 23."  But if I subtract 23 from the left-hand side of the equation, I have to do the same to the right-hand side.
 
So
 
x + 23 - 23 = 45 - 23
 
x = 22