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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

### 2 Answers by Expert Tutors

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
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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