Plus and Minus (Same Variables)

When you add variables together, you’re actually using the definition of multiplication. In other words: $x+x=2x$ and

The same applies to subtraction, $-x-x-x=-3x$. Remember that $x-x=0$. Below is an example of how you can add and subtract the same variables.

Example 1

Calculate and simplify

 $x+x-x-x-x+x+x$

There are several ways to do this, and you’ll look at two separate methods. The first is to add the positive and negative $x$s separately:

$\begin{array}{llll}\hfill & \phantom{=}x+x-x-x-x+x+x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =x+x+x+x-x-x-x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\underset{4-3=1}{\underbrace{4x-3x}}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Note! You write $1x=x$.

Another method is to rearrange the terms so you have minus against plus, so you can cancel them with each other:

$\begin{array}{llll}\hfill & \phantom{=}x+x-x-x-x+x+x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =x-x+x-x+x-x+x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{x}-\text{x}+\text{x}-\text{x}+\text{x}-\text{x}+x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =x\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

It’s not always the case that the variables in an expression are the same. When there are different variables in an expression, you can’t perform the calculation like you did in the example above.