1.04  Linear Equations

Intermediate Algebra: One Step at a Time,  Page 41:   #3, 5, 6, 7, 8.

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

To see Section 1.04, with explanations, examples, exercises, and answers, click here!

3.   Solve for x:          .

Solution:  First, remove parentheses by the distributive property.

Next, combine like terms on the right side. 

Get all the x terms on the left side by adding  to each side.

Next, subtract 18 from each side:

Divide by 8:                            

Since you can solve for x and get at least one solution, this is called a CONDITIONAL EQUATION, and the solution is .

5.   Solve for x:          .

Solution:  First, remove parentheses by the distributive property.

Next, combine like terms on the left side. 

This equation is ALWAYS TRUE, since  always equals , so this is an IDENTITY!  The answer is therefore All values of x or All REAL values of x.

NOTE:  You could have continued one more step by subtracting  from each side.  This would leave the equation  .  Since there are NO variables left in the equation, it will be either always true or always false.   In this case the equation is TRUE, so this is an IDENTITY.  The solution is ALL VALUES of x.

6.   Solve for x:          .

Solution:  First, remove parentheses by the distributive property.

You can subtract  from each side, eliminating all the  terms.

Add  to each side:

Divide by :                         

Since you can solve for x and get at least one solution, this is called a CONDITIONAL EQUATION, and the solution is  .

7.   Solve for x:          .

Solution:  First, remove parentheses by the distributive property.

You can subtract  and add  to each side,.

All the variables subtract out, leaving:

This equation is FALSE!  Since the equation is false, the equation is a CONTRADICTION, and there is NO SOLUTION.

8.   Solve for x:          .

Solution:  First, remove parentheses by the distributive property.

You can subtract  from each side, eliminating all the  terms.

Divide by :                 

Since you can solve for x and get at least one solution, this is called a CONDITIONAL EQUATION, and the solution is .

Return to main page        Math in Living C O L O R !!

     Return to Basic Algebra page     Return to Intermediate Algebra page  

 Return to College Algebra page