Examples
Divide both sides by 5 or multiply both sides by
Find practice problems and solutions at Linear Equations Practice Problems  Set 2.
4 Step Method for Solving Linear Equations
Some equations can be solved in a number of ways. However, the general method in this book will be the same:
 Simplify both sides of the equation.
 Collect all terms with variables in them on one side of the equation and all nonvariable terms on the other (this is done by adding/subtracting terms).
 Factor out the variable.
 Divide both sides of the equation by the variable’s coefficient (this is what has been factored out in step 3).
Of course, you might need only one or two of these steps. In the previous examples and practice problems, only step 4 was used.
In the following examples, the number of the step used will be in parentheses. Although it will not normally be done here, it is a good idea to verify your solution in the original equation.
Examples
Find practice problems and solutions at Linear Equations Practice Problems  Set 3.
Simplifying Fractions and Using the Associative Property to Solve Linear Equations
When the equation you are given has fractions and you prefer not to work with fractions, you can clear the fractions in the first step. Of course, the solution might be a fraction, but that fraction will not occur until the last step. Find the LCD of all fractions and multiply both sides of the equation by this number. Then, distribute this quantity on each side of the equation.
Examples
Common Mistakes
A common mistake is to fail to distribute the LCD. Another is to multiply only one side of the equation by the LCD.
In the first example, , one common mistake is to multiply both sides by 5 but not to distribute 5 on the lefthand side.
Another common mistake is not to multiply both sides of the equation by the LCD.
In each case, the last line is not equivalent to the first line—that is, the solution to the last equation is not the solution to the first equation.
Using the Associative Property to Solve Linear Equations
In some cases, you will need to use the associative property of multiplication with the LCD instead of the distributive property.
Example
On each side, there are three quantities being multiplied together. On the left, the quantities are 6, and x + 4. By the associative law of multiplication, the 6 and can be multiplied, then that product is multiplied by x + 4. Similarly, on the right, first multiply 6 and , then multiply that product by x – 1.
Find practice problems and solutions at Linear Equations Practice Problems  Set 4.
More practice problems for these concepts can be found at: Algebra Linear Equations Practice Test.
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