Solving Linear Equations: Part 3

Introduction

We have explored various techniques for solving linear equations. We now wish to consider linear equations with one or more fractions. Our approach to linear equations with fractions will be to first eliminate the fractions and then to use known techniques to solve the linear equation.






Steps for Solving Linear Equations with Fractions

Step 1: Find the Least Common denominator of all of the fractions in the linear equation.

Step 2: Multiply both sides of the equation by this least common denominator to eliminate all fractions.

Step 3: Solve the linear equation using one of the already discussed techniques.




Examples

Example 1:

 

 

Step 1: Find the Least Common denominator of all of the fractions in the linear equation.

The Least Common Denominator of 2,3 and 4 is 12.

Step 2: Multiply both sides of the equation by this least common denominator to eliminate all fractions.

 

 

 

 

Step 3: Solve the linear equation using one of the already discussed techniques.

 

 

 

 

 




Example 2:

 

 

Step 1: Find the Least Common denominator of all of the fractions in the linear equation.

The Least Common Denominator of 2,3 and 6 is 6.

Step 2: Multiply both sides of the equation by this least common denominator to eliminate all fractions.

 

 

 

 

 

Step 3: Solve the linear equation using one of the already discussed techniques.

 

 

 

 

 








Practice step by step below:

 

Click below to practice solving problems: