SOLVING LINEAR EQUATIONS

Recall the following:

• A linear equation is a polynomial of degree 1.
• In order to solve for the unknown variable, you must isolate the variable
• In the order of operations, multiplication and division are completed before addition and subtraction.

LINEAR EQUATION - Solve for x in the following equation.

Example 1:

Complete multiplication.

Group like terms on each side of the equal sign.

Subtract 18 x from both sides of the equation.

Subtract 57 from both sides of the equation.

Divide both sides of the equation by 12 and simplify.

The answer is

Check the solution by substituting in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

• Left Side:

  

  

• Right Sides:

  

  

Since the left side of the original equation equals the right side of the original equation when the value is substituted for x, the solution x = is verified.

You can also check the answer with your calculator.

• Left Side:

  

  

• Right Sides:

  

  
  

  
  

  
  You can also check the answer by graphing

  

  (left side of original equation minus right side of original equation). The x-intercept is -5.25.

  If you would like to review another example, click on Example

  If you would like to test yourself by working some problems similar to this example, click on Problem.

  If you would like to go back to the equation table of contents, click on Contents.

  
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