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:

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

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