Equation-Solving Main Menu

 

LINEAR EQUATIONS

A linear equation is one that can be expressed in the form: 

Ax + B = 0

Linear equations are also called first degree equations because a linear equation consists of polynomial expressions in which the highest degreed term is one.

 

Definition
 
Examples

EXAMPLES OF LINEAR EQUATIONS

       
 

 

Example 1

 

 

Example 2

 

 

2(x - 4) + 5x = -22


Solving

STEPS TO SOLVE A LINEAR EQUATION

  1. Clear fractions by multiplying all terms by the lowest common denominator.
  2. Simplify the algebraic expression on each side.
    • remove parentheses using the distributive property
    • Combine all like terms
  3. Collect all the variable terms to one side and all the constant terms to the other side.
    • add/subtract variable terms to both sides of the equation
    • add/subtract constant terms to both sides of the equation
  4. Divide both sides of the equation by the coefficient of the variable.
  5. Check the answer in the original equation.

Sample Problems

Sample Problem 1

 

2(x - 4) + 5x = - 22

 

2x - 8 + 5x = - 22

7x - 8 = - 22
   
+ 8     + 8

7x = - 14

x = - 2

CHECK:  2(x - 4) + 5x = - 22

2(-2 - 4) + 5(-2)  = - 22 (?)

2(-6) + 5(- 2) = - 22

-12 - 10 = - 22

-22 = - 22  ü

Simplify the algebraic on each side.  Here we begin by removing the parentheses.

 


Combine like terms

 

Isolate the variable to one side. Here, add 8 to both sides.

Divide both sides by the coefficient of the variable.

This is the proposed solution. Now check in the original equation to verify.
CHECK:
Replace the solution in for the variable where ever the variable appears.

Work each side of the separately using the order of operations.

Both sides must be the same.

Sample Problems

Sample Problem 2

 





5(3x) = 2x - 78

15x = 2x - 78
 -2x   -2x         

13x = - 78

13x = - 78
13        13

x = - 6

CHECK

ü


Multiply both sides of the equation by 10 to clear all fractions.

 

 

 

 
Simplify each side


Isolate the variable to one side



Divide both sides by 13

 


The proposed solution is 6.

CHECK

Replace the solution in for the variable where ever the variable appears.

Work each side of the separately using the order of operations.

Both sides must be the same.