Solving Two-Step Equations

A two-step equation is as straightforward as it sounds. You will need to perform two steps in order to solve the equation.

One goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The other goal is to have the number in front of the variable equal to one. The variable does not always have to be x. These equations can make use of any letter as a variable.

The strategy for getting the variable by itself with a coefficient of 1 involves using opposite operations. For example, to move something that is added to the other side of the equation, you should subtract. The most important thing to remember in solving a linear equation is that whatever you do to one side of the equation, you MUST do to the other side. So if you subtract a number from one side, you MUST subtract the same value from the other side. You will see how this works in the examples.

In solving two-step equations you will make use of the same techniques used in solving one-step equation only you will perform two operations rather than just one.

Let's Practice:

1. Solve

This problem does not have the variable by itself on one side. We need to get rid of the 4 that is added, so we’ll need to subtract 4 from both sides. Even after doing that, there is still a 3 multiplied by the variable, so division will be necessary to eliminate it.

2. Solve

The variable is not by itself on one side. We will get rid of the 5 that is added by subtracting 5 from both sides. This still leaves a -2 in front of the variable so we will have to divide both sides by -2.

3. Solve

As in the previous example, the variable is not by itself on one side. We will need to get rid of the -5 by adding 5 to both side. We will then need to multiply both sides by the reciprocal of which is .

 http://www.algebralab.org/lessons/lesson.aspx?file=algebra_onevariabletwostep.xml