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 3:

Get rid of the denominators by multiplying both sides by 24, the smallest number that 3,8, and 6 will divide into evenly.

Recall the line that separates the numerator and the denominator also functions as a parenthesis. It instructs the reader to treat the numerator as one number and the denominator as one number.

Simplify:

Subtract 12x from both sides of the equation and subtract 78 from both sides of the equation:

The answer is x=6.

Check the solution by substituting 6 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 Side:

Since the left side of the original equation equals the right side of the original equation after you substitute x=6, the answer x=6.

You can also check your answer by graphing (left side of the original equation minus the right side of the original equation). The x-intercept is 6.

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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