Algebra Tutorials
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Solving Linear Equations with Integer Coefficients

We will start with an example that contains only one term with the variable we are trying to solve for.

In this example there is only one copy of the x-term that we are trying to solve for. To isolate x, we must remove the terms with no x-variable by performing their inverse operation. In this case we need to subtract the 6 first.

 

 

 

 

 

 

 

In this example there are terms that contain x on both sides of the equation.
The first step will be to use the addition property of equality to remove the variable term on the right side so that we are left with only one copy of x on the left side.

 

 

 

To "solve for x" we must follow these steps:

1. make sure all variable terms are on one side and all constant terms are on the other
2. then divide both sides by coefficent of x to completely isolate x, leaving "x = "

In the last two examples the constants in the equations were integers. If the equation contains fractions, then the first step would be to remove all the fractions by multiplying both sides of the equation by the LCD of all fractions in the equation. This will turn all coefficients and constants in the equation into integers. If you need help on this, see the section marked "equations with fractions".