Equations

UK Secondary (7-11)

Balancing equations

Lesson

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

- look exactly the same on both sides, like this one:

or

- the left and right side will look different, but there is a value for the variable which will make both sides equal, like this one which works if the value of $x$
`x`is equal to $2$2, because the left hand side becomes $3\times2$3×2 which is $6$6 and the right hand side becomes $2+4$2+4 which is also $6$6.

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 variable, then we simply need to make sure that both sides have the same constant value and the same variable 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{}$2`v`+5=2`v`+

**Think**: Both sides need to have the same value. We will compare the constant value and the coefficients of the variable $v$`v`.

**Do**:

Fill in the blank to balance the equation: $3m+4=m+\editable{}$3`m`+4=`m`+

**Think**: Both sides need to have the same value. I will compare the constant value and the coefficients of the variable $m$`m`.

**Do**:

Fill in the blank to balance the equation: $2x-6=2x-10+\editable{}$2`x`−6=2`x`−10+