You can think of an equation as a balanced scale, with the equals sign in the middle.
Whatever is on the left must equal whatever is on the right.
If we add or subtract something on just one side of the equation, the scale will become unbalanced.
Similarly, if we divide or multiply on only one side of the equation, the scale will become unbalanced.
We keep the scale, and the equation, in balance by making sure that whatever operation we do to one side, we also do exactly the same to the other side.
A balanced equation will either
or
If we need to balance an equation, then we need to make both sides have the same value. If we do not know the value of a variable or pronumeral, then we simply need to make sure that both sides have the same constant value and the same pronumeral values. Make them look the same!
Let's have a look at some examples.
Fill in the blank to balance the equation: $2v+5=2v+\editable{}$2v+5=2v+
Think: Both sides need to have the same value. We will compare the constant value and the coefficients of the pronumeral $v$v.
Do:
Fill in the blank to balance the equation: $3m+4=m+\editable{}$3m+4=m+
Think: Both sides need to have the same value. I will compare the constant value and the coefficients of the pronumeral $m$m.
Do:
Fill in the blank to balance the equation: $2x-6=2x-10+\editable{}$2x−6=2x−10+