How is solving an equation like maintaining a balance on a pan balance? How is it different?

Question

nothing additional

Answer 1

A pan balance (or balance scale) has three results:  level (equal), heavy, or light.

 

"maintaining a balance" means that it is balanced (that is, equal) when it starts.  This is how an equation looks to us when the problem describes an equation to be solved.  To "solve," we must find the value of a variable in the equation by making changes to the equation.

 

The most important rule is:

   When equal amounts are either added, subtracted, divided, or multiplied by equal amounts, the results are equal.

 

This means that we look at an equation and determine how to get the variable by itself (usually on the left side) and the solution on the right side of the equal sign.  The operation we perform and the value we use is the opposite of the one in the equation.  That eliminates that value on that side of the equation.

    Example:

       Problem gives:  2x = 6           [note: x is multiplied by 2]

       Operation:   divide both sides by 2

       Solution:            x = 3

 

Can you think of how it is different?