Language:

You’ve learned how to get rid of a term on one side of an equation. But what do you do when you’re left with a number—known as a coefficient—in front of $x$? We’ll take a look at this situation below.

Rule

- 1.
- Move all the terms containing only numbers over to one side. Remember to change signs.
- 2.
- Move all terms containing the variable—$x$, for example—to the other side. Remember to change signs.
- 3.
- Simplify both sides.
- 4.
- Divide both sides by the number in front of $x$, known as its coefficient.

Let’s take a look at an example and see what this looks like:

Example 1

$$\begin{array}{llll}\hfill 2x+3& =7\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 2x& =7-3\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 2x& =4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{2x}{2}& =\frac{4}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill \frac{\text{2}x}{\text{2}}& =\frac{4}{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill x& =2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$