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

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2 Answers

 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
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.
x + 23 - 23 = 45 - 23
x = 22