How to balance equation

Question

How to balance equation example 

 

Answer 1

This depends on the kind of equation

 the esential idea is to always do the same thing to both sides of the equation.  What you do and when you do it is based on what is in the problem.  we first make sure that all pieces of a variable are on the same side.  We do that by distributing and adding pieces. and we simplify as much as we can

 then we cancel anything that is not the variable we are solving for in reverse order of operations

order of operations is Parenthesis exponents multiplication division addition subtraction if you recall.

here is an example

5(x+3)+7=4x+1

First we distribute so we can simplify what we can through addition on each side

5x+5*3+7=4x+1

5x+15+7=4x+1

5x+22=4x+1

then we want the variable on the same side of the equation.  to do that, we subtract the smallest term with x in it from both sides

5x+22=4x+1

-4x        -4x

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x+22=1

then we cancel what is added to x since it is first in the order for what we need to cancel

x+22=1

  -22    -22

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x=-21

if we had something multiplied to x we would then divide it.

Does that suit your needs or do you need something else?