solve x - 12 =7 using algebraic operations

Question

Solve x - 12 =7

Answer 1

Algebraic operations is just another way of saying algebraic manipulations.

 

x - 12 = 7 needs to be solved.  To solve for the variable 'x', it needs to be isolated.

 

If you do something to one side of an equation and you do the same thing to the other side, is the equation changed?

No.  The equation remains the same whether you multiply, divide, add, subtract, raise to a power, take a root of a power, or a whole bunch more stuff you can do later on. e.g. (1 = 1, if you add 1 to both sides, will 2 = 2? Yes. What about multiplying by 5? will the = sign still be true? Yes.)

 

To isolate the variable x, you need to get rid of that pesky - 12  :  

 

If you add 12 to - 12, what do you get?  You get 0.  

So if you do something to one side of the equation, you MUST do the same thing to the other side.  

By adding 12 to both sides you now have:

 

x + 12 - 12 = +12 +  7

 

Now you can simply write the left side of the equation as:

 x = 12 + 7

All that is left is to add 12 and 7 and you end up with 19.

Now write 19 on the right side of the equation and you have:

x = 19

Answer 2

x - 12 = 7     add 12 to both sides

x = 19

{19}