Solving Linear (1st degree) Equations

There are basically 6 steps to solving equations.  Not all steps need to be used within any given problem.  The six steps to solving a linear equation are

(1) Fractions (can be removed by the use of the LCD)
(2) Distribute (if parenthesis are in the equation)
(3) Collect (like terms)
(4) Addition (or subtraction) to move terms
(5) Multiplication (or division) to move factors
(6) Check

If there are fractions within the equation then multiply each of the terms by the LCD (the smallest number that all of the denominators will divide into the LCD evenly.)  Add, subtract, multiply or divide anything to the terms of the equation as long the operation is performed “equally” to both sides of the equation (in other words do the same operation/s with the same number/s) to both sides of the equation.  The goal in solving an equation is to isolate the variable … get the variable (letter) on one side of the equation with no coefficient (no number in front of the variable.)  In essence isolating the variable means to “disconnect” the numbers that are attached to the variable.  If a number is connected by addition or subtraction, then (respectively) “undo” this by subtracting or adding.  If the variable has a coefficient (number attached by multiplication) then divide the coefficient.

Example (1), involves all of the steps … except fractions.  Example (2)  has a “simple” fraction.
Example (3) has a more difficult fraction.

(1) Solve:             


                                              …the results

 =                        …Collect

                                                 …Addition (and subtraction)

                                                                   …the results


     *                                   …the solution


                  Check…substitute the number found into the      
                           original equation and see if the left side is 
                                   equal to the right side.  If this turns out to

                                           be true, then this number is the correct answer.

            J Correct



(2) Solve:                                          

                           …Multiply both sides by the reciprocal to the   

                                                  fraction that is attached to the variable




       J Correct


(3) Solve:                                        …Fractions L

              …Multiply each term by the LCD = 12

                               =                             …the results of multiplication of terms


                                            …the results of Addition








              J Correct

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 09-Jan-2014