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Linear Equations Help (page 2)

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By — McGraw-Hill Professional
Updated on Sep 26, 2011

Examples

Divide both sides by 5 or multiply both sides by Factoring To Reduce Fractions Examples

Factoring To Reduce Fractions Examples

Factoring To Reduce Fractions Examples

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:

  1. Simplify both sides of the equation.
  2. 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).
  3. Factor out the variable.
  4. 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

Factoring To Reduce Fractions 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

Factoring To Reduce Fractions 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, Factoring To Reduce Fractions Examples , one common mistake is to multiply both sides by 5 but not to distribute 5 on the left-hand side.

Factoring To Reduce Fractions Examples

Another common mistake is not to multiply both sides of the equation by the LCD.

Factoring To Reduce Fractions Examples

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

Factoring To Reduce Fractions Example

On each side, there are three quantities being multiplied together. On the left, the quantities are 6, Factoring To Reduce Fractions Example and x + 4. By the associative law of multiplication, the 6 and Factoring To Reduce Fractions Example can be multiplied, then that product is multiplied by x + 4. Similarly, on the right, first multiply 6 and Factoring To Reduce Fractions Example , then multiply that product by x – 1.

Factoring To Reduce Fractions Example

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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